Exam 7: Right Triangles and Vectors

The impedance of an electric circuit can be modelled by a right angle triangle. The hypotenuse is the impedance, the opposite side is the reactance, and the adjacent side is the resistance of the circuit. Given an impedance of $476 \Omega$ at an angle of $24^{\circ}$ , find the reactance and the reactance.

(Short Answer)

4.9/5

(29)

Question 21

Express $\cot 3 \pi / 8$ as a function of the complementary angle.

(Short Answer)

4.7/5

(31)

Question 22

Determine the value of $\theta$ to 3 significant digits if $\cot \theta=24.7$ .

(Short Answer)

4.7/5

(31)

Question 23

Evaluate $\tan 16.5^{\circ}$ to 2 significant digits.

(Short Answer)

4.7/5

(32)

Question 24

What is $168.475^{\circ}$ in degrees, minutes, and seconds?

(Short Answer)

4.7/5

(42)

Question 25

Express $\cos \pi / 4$ as a function of the complementary angle.

(Short Answer)

4.8/5

(33)

Question 26

Convert 1.74 rev to radians.

(Short Answer)

4.9/5

(43)

Question 27

Express $\csc 34.3^{\circ}$ as a function of the complementary angle.

(Short Answer)

4.7/5

(38)

Question 28

Find the resultant of $346 / \underline{147^{\circ}}$ and $563 / \underline{72.6^{\circ}}$ .

(Short Answer)

4.8/5

(23)

Question 29

Vectors $\mathbf{A}$ and $\mathbf{B}$ meet at right angles. Vector $\mathbf{A}$ has a magnitude of 678 and vector $\mathbf{B}$ has a magnitude of 876 . Calculate the angle the resultant makes with $\mathbf{B}$ .

(Short Answer)

4.7/5

(33)

Question 30

Draw $262 / \underline{76.5^{\circ}}$ on coordinate axes.

(Essay)

4.8/5

(35)

Question 31

Evaluate $\cos 74.6^{\circ}$ to 4 decimal places.

(Short Answer)

5.0/5

(35)

Question 32

Express $\tan 62^{\circ}$ as a function of the complementary angle.

(Short Answer)

4.9/5

(30)

Question 33

Evaluate to three significant digits: $5.7 \tan 2.8^{\circ}+13.3 \sin 6.7^{\circ}$

(Short Answer)

4.9/5

(29)

Question 34

The angle of elevation of the top of a building from a point on the ground $86 \mathrm{~m}$ from its base is $34.6^{\circ}$ . Find the height of the building.

(Short Answer)

4.7/5

(40)

Question 35

Determine the value of $\theta$ (in radians) given that the opposite side is $6.5 \mathrm{~cm}$ and the hypotenuse is $8.3 \mathrm{~cm}$ .

(Short Answer)

4.9/5

(43)

Question 36

If $\mathbf{V}_{\mathbf{y}}=17.5$ and $\mathbf{V}$ makes an angle of $42.0^{\circ}$ with the $x$ -axis, find $\mathbf{V}_{\mathbf{x}}$ .

(Short Answer)

5.0/5

(38)

Question 37

Given $\theta=1.5 \mathrm{rad}$ , calculate $\sin \theta, \cos \theta$ , and $\tan \theta$ to 4 decimal places.

(Essay)

4.9/5

(37)

Question 38

Given a right triangle with hypotenuse $164 \mathrm{~cm}$ long and an adjacent side $128 \mathrm{~cm}$ long, find the angle and the length of the opposite side.

(Short Answer)

4.8/5

(36)

Question 39

Write $\sin \theta, \cos \theta$ , and $\tan \theta$ to 3 significant digits: $\theta=58^{\circ} 18^{\prime} 45^{\prime \prime}$

(Essay)

4.8/5

(35)

Question 40

Exam 7: Right Triangles and Vectors

Express cot⁡3π/8\cot 3 \pi / 8cot3π/8 as a function of the complementary angle.

Determine the value of θ\thetaθ to 3 significant digits if cot⁡θ=24.7\cot \theta=24.7cotθ=24.7 .

Evaluate tan⁡16.5∘\tan 16.5^{\circ}tan16.5∘ to 2 significant digits.

What is 168.475∘168.475^{\circ}168.475∘ in degrees, minutes, and seconds?

Express cos⁡π/4\cos \pi / 4cosπ/4 as a function of the complementary angle.

Convert 1.74 rev to radians.

Express csc⁡34.3∘\csc 34.3^{\circ}csc34.3∘ as a function of the complementary angle.

Find the resultant of 346/147∘‾346 / \underline{147^{\circ}}346/147∘​ and 563/72.6∘‾563 / \underline{72.6^{\circ}}563/72.6∘​ .

Vectors A\mathbf{A}A and B\mathbf{B}B meet at right angles. Vector A\mathbf{A}A has a magnitude of 678 and vector B\mathbf{B}B has a magnitude of 876 . Calculate the angle the resultant makes with B\mathbf{B}B .

Draw 262/76.5∘‾262 / \underline{76.5^{\circ}}262/76.5∘​ on coordinate axes.

Evaluate cos⁡74.6∘\cos 74.6^{\circ}cos74.6∘ to 4 decimal places.

Express tan⁡62∘\tan 62^{\circ}tan62∘ as a function of the complementary angle.

Evaluate to three significant digits: 5.7tan⁡2.8∘+13.3sin⁡6.7∘5.7 \tan 2.8^{\circ}+13.3 \sin 6.7^{\circ}5.7tan2.8∘+13.3sin6.7∘

The angle of elevation of the top of a building from a point on the ground 86 m86 \mathrm{~m}86 m from its base is 34.6∘34.6^{\circ}34.6∘ . Find the height of the building.

Determine the value of θ\thetaθ (in radians) given that the opposite side is 6.5 cm6.5 \mathrm{~cm}6.5 cm and the hypotenuse is 8.3 cm8.3 \mathrm{~cm}8.3 cm .

If Vy=17.5\mathbf{V}_{\mathbf{y}}=17.5Vy​=17.5 and V\mathbf{V}V makes an angle of 42.0∘42.0^{\circ}42.0∘ with the xxx -axis, find Vx\mathbf{V}_{\mathbf{x}}Vx​ .

Given θ=1.5rad\theta=1.5 \mathrm{rad}θ=1.5rad , calculate sin⁡θ,cos⁡θ\sin \theta, \cos \thetasinθ,cosθ , and tan⁡θ\tan \thetatanθ to 4 decimal places.

Given a right triangle with hypotenuse 164 cm164 \mathrm{~cm}164 cm long and an adjacent side 128 cm128 \mathrm{~cm}128 cm long, find the angle and the length of the opposite side.

Write sin⁡θ,cos⁡θ\sin \theta, \cos \thetasinθ,cosθ , and tan⁡θ\tan \thetatanθ to 3 significant digits: θ=58∘18′45′′\theta=58^{\circ} 18^{\prime} 45^{\prime \prime}θ=58∘18′45′′

Numerical Computation

Introduction to Algebra

Simple Equations and Word Problems

Functions

Graphs

Geometry

Factors and Factoring

Fractions and Fractional Equations

Systems of Linear Equations

Determinants

Matrices

Exponents and Radicals

Quadratic Equations

Oblique Triangles and Vectors

Radian Measure, Arc Length, and Circular Motion

Graphs of the Trigonometric Functions

Trigonometric Identities and Equations

Ratio, Proportion, and Variation

Exponential and Logarithmic Functions

Complex Numbers

Analytic Geometry

Binary, Hexadecimal, Octal, and Bcd Numbers

Inequalities and Linear Programming

Sequences, Series, and the Binomial Theorem

Introduction to Statistics and Probability

Derivatives of Algebraic Functions

Graphical Applications of the Derivative

Applied Applications of the Derivative

Integration

Applications of the Integral

More Applications of the Integral

Derivatives of Trigonometric, Logarithmic, and Exponential Functions

Methods of Integration

Differential Equations

Solving Differential Equations by the Laplace Transform and by Numerical Methods

Infinite Series

Filters

Express $\cot 3 \pi / 8$ as a function of the complementary angle.

Determine the value of $\theta$ to 3 significant digits if $\cot \theta=24.7$ .

Evaluate $\tan 16.5^{\circ}$ to 2 significant digits.

What is $168.475^{\circ}$ in degrees, minutes, and seconds?

Express $\cos \pi / 4$ as a function of the complementary angle.

Express $\csc 34.3^{\circ}$ as a function of the complementary angle.

Find the resultant of $346 / \underline{147^{\circ}}$ and $563 / \underline{72.6^{\circ}}$ .

Vectors $\mathbf{A}$ and $\mathbf{B}$ meet at right angles. Vector $\mathbf{A}$ has a magnitude of 678 and vector $\mathbf{B}$ has a magnitude of 876 . Calculate the angle the resultant makes with $\mathbf{B}$ .

Draw $262 / \underline{76.5^{\circ}}$ on coordinate axes.

Evaluate $\cos 74.6^{\circ}$ to 4 decimal places.

Express $\tan 62^{\circ}$ as a function of the complementary angle.

Evaluate to three significant digits: $5.7 \tan 2.8^{\circ}+13.3 \sin 6.7^{\circ}$

The angle of elevation of the top of a building from a point on the ground $86 \mathrm{~m}$ from its base is $34.6^{\circ}$ . Find the height of the building.

Determine the value of $\theta$ (in radians) given that the opposite side is $6.5 \mathrm{~cm}$ and the hypotenuse is $8.3 \mathrm{~cm}$ .

If $\mathbf{V}_{\mathbf{y}}=17.5$ and $\mathbf{V}$ makes an angle of $42.0^{\circ}$ with the $x$ -axis, find $\mathbf{V}_{\mathbf{x}}$ .

Given $\theta=1.5 \mathrm{rad}$ , calculate $\sin \theta, \cos \theta$ , and $\tan \theta$ to 4 decimal places.

Given a right triangle with hypotenuse $164 \mathrm{~cm}$ long and an adjacent side $128 \mathrm{~cm}$ long, find the angle and the length of the opposite side.

Write $\sin \theta, \cos \theta$ , and $\tan \theta$ to 3 significant digits: $\theta=58^{\circ} 18^{\prime} 45^{\prime \prime}$