Exam 8: Trigonometric Identities and Equations

Graph the expression on each side of the equals symbol to determine whether the equation might be an identity. - $1 + \tan ^ { 2 } x = \frac { \cos ^ { 2 } x } { 1 - \cos ^ { 2 } x }$

Use Identities to find the exact value. - $\cos 36 ^ { \circ } \cos 24 ^ { \circ } - \sin 36 ^ { \circ } \sin 24 ^ { \circ }$

Verify that the equation is an identity. - $\cot ( x + y ) \cot ( x - y ) = \frac { 1 - \tan ^ { 2 } x \tan ^ { 2 } y } { \tan ^ { 2 } x - \tan ^ { 2 } y }$

Use the fundamental identities to simplify the expression. - $\frac { \sin x \cos x } { \tan x }$

Solve the equation for exact solutions. - $\cos ^ { - 1 } x = \sin ^ { - 1 } \frac { 4 } { 5 }$

Determine all solutions of the equation in radians. -Find $\tan \frac { x } { 2 }$ , given that $\tan x = - 3$ and $x$ terminates in $90 ^ { \circ } < x < 180 ^ { \circ }$ .

Use a calculator to give the value to the nearest degree. - $\theta = \sin ^ { - 1 } ( 0.8830 )$

Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression. - $\frac { \csc x \cot x } { \sec x }$

The statement tan-1(tan x) = x for all real numbers in the interval -On the given graph of y $y = \cot x$ cot x sketch the graph of y $y = \cot ^ { - 1 } x$ x as defined in the text. Give the domain and the range.

Use identities to find the indicated value for each angle measure. - $\sin \theta = - \frac { 4 } { 5 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cos ( 2 \theta )$

Provide an appropriate response. -The statement sin $\sin ^ { - 1 } ( \sin x ) = x$ x for all real numbers in the interval $0 \leq \mathrm { X } \leq \pi$

Use the fundamental identities to simplify the expression. - $\frac { \cos ^ { 2 } \theta } { \sin ^ { 2 } \theta } + \csc \theta \sin \theta$