Exam 26: Trigonometric Functions of Any Angle

The displacement from equilibrium of an oscillating weight suspended by a spring is given by​ $y = 2 \cos 6 t$ ,where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when $t = \frac { 1 } { 8 }$ .(Round your answers to two decimal places. )​ ​ ​

The displacement from equilibrium of an oscillating weight suspended by a spring is given by​ $y = 2 \cos 6 t$ ​ where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when $t = 7$ .(Round your answers to nearest tenth. )​ ​

The point is on the terminal side of an angle in standard position.Determine the exact values of the three trigonometric functions sine,cosine,and tangent of the angle θ.​ $( 5,12 )$ ​

Given the equation below,determine two solutions such that $0 ^ { \circ } < \theta < 360 ^ { \circ }$ . ​cos θ = $- \frac { \sqrt { 3 } } { 2 }$

Evaluate the trigonometric function.Round your answer to four decimal places.​ $\cot \left( - \frac { 13 \pi } { 5 } \right)$ ​

Evaluate the trigonometric function.Round your answer to four decimal places.(Be sure the calculator is set in the correct angle mode. ) ​ Tan 4.9 ​

The current I (in amperes)when 100 volts is applied to a circuit is given by​ $I = 5 e ^ { - 2 t } \sin t$ ​ where t is the time (in seconds)after the voltage is applied.Approximate the current at T = 0.8 second after the voltage is applied.(Round your answers to two decimal places. ) ​

Evaluate the trigonometric function.Round your answer to four decimal places.​ $\tan \left( - \frac { \pi } { 8 } \right)$ ​

Evaluate the trigonometric function.Round your answer to four decimal places.​ $\tan \left( \frac { \pi } { 3 } \right)$ ​

Determine the exact value of $\csc \theta$ when $\cot \theta = \frac { 20 } { 21 }$ and $\csc \theta$ < 0.

Find the reference angle $\theta ^ { \prime }$ ,and sketch $\theta$ and $\theta ^ { \prime }$ in standard position.​ $\theta = \frac { 8 \pi } { 7 }$ ​

Evaluate the trigonometric function.Round your answer to four decimal places. ​ Cot 3.35 ​

Use a calculator to evaluate $\sin 5 ^ { \circ }$ .Round your answer to four decimal places.