Deck 6: Analytic Trigonometry

Question 1

Use the product-to-sum formulas to rewrite the product as a sum or difference.
​ $10 \cos 55 ^ { \circ } \cos 25 ^ { \circ }$ ​

Answer 1

$5 \left( \cos 30 ^ { \circ } + \cos 80 ^ { \circ } \right)$

Question 2

Use the sum-to-product formulas to rewrite the sum or difference as a product.
​ $\sin ( 7 \theta ) + \sin ( 5 \theta )$ ​

Answer 2

$2 \sin ( 6 \theta ) \cos \theta$

Question 3

Evaluate the following expression.
​ $\cot ^ { 2 } t \left( 4 \sec ^ { 2 } t - 4 \right)$ ​

Answer 3

4

Question 4

Use the Quadratic Formula to solve the given equation on the interval $\left[ 0 , \frac { \pi } { 2 } \right)$ ; then use a graphing utility to approximate the angle x. Round answers to three decimal places.
​ $18 \tan ^ { 2 } x - 13 \tan x + 2 = 0$ ​

Question 5

Find the expression as the sine or cosine of an angle.
​ $\cos 100 ^ { \circ } \cos 50 ^ { \circ } - \sin 100 ^ { \circ } \sin 50 ^ { \circ }$ ​

Question 6

Evaluate the following expression. ( $x \neq \pi n$ , where n is a whole number)
​ $\frac { 8 \csc ( - 3 x ) } { \sec ( - 3 x ) }$ ​

Question 7

Convert the expression.
​ $\tan \left( \frac { u } { 2 } \right)$ ​

Question 8

Find the exact value of the given expression.
​ $\sin \left( \frac { \pi } { 3 } - \frac { 3 \pi } { 4 } \right)$ ​

Question 9

Use the figure to find the exact value of the trigonometric function.
​ $\sin ( 2 \theta )$ ​ ​ $a = 1$ , $b = 8$ ​

Question 10

Simplify the expression algebraically.
​ $\cos ( 2 x + 4 y ) \cos ( 2 x - 4 y )$ ​

Question 11

Find the exact value of $\sec \left[ \sin ^ { - 1 } \left( \frac { 8 } { 17 } \right) \right]$ .

Question 12

Convert the expression.
​ $\cos ( 10 \alpha )$ ​

Question 13

Use inverse functions where needed to find all solutions of the equation in the interval $[ 0,2 \pi )$ .
​ $\sec ^ { 2 } x - 5 \sec x = 0$ ​

Question 14

Use the product-to-sum formulas to rewrite the product as a sum or difference.
​ $\sin \left( \frac { \pi } { 5 } \right) \cos \left( \frac { \pi } { 10 } \right)$ ​

Question 15

Use the cofunction identities to evaluate the expression without using a calculator.
​ $\sin ^ { 2 } 40 ^ { \circ } + \sin ^ { 2 } 50 ^ { \circ }$ ​