Exam 34: Sum and Difference Formulas

Use a graphing utility to select the correct graph of ​ $y _ { 1 }$ and $y _ { 2 }$ in the same viewing window.Use the graphs to determine whether $y _ { 1 } = y _ { 2 }$ .Explain your reasoning.​ $y _ { 1 } = \cos ( x + 4 ) , y _ { 2 } = \cos x + \cos 4$ ​

Simplify the expression algebraically.​ $\sin ( 7 x + 7 y ) + \sin ( 7 x - 7 y )$ ​

Simplify the expression algebraically.​ $\cos ( 6 x + 9 y ) + \cos ( 6 x - 9 y )$ ​

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ,where $C = \arctan ( a / b ) , a = 13 , b = 6 , B = 3$ to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

Simplify the following expression algebraically.​ $7 \cos ( \pi + x )$ ​

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ ,where $C = \arctan ( b / a ) , a = 5 , b = 8 , B = 1$ ,to rewrite the trigonometric expression in the following form.​ $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ ​ $a \sin B \theta + b \cos B \theta$ ​

Find the expression as the cosine of an angle. ​​ $\cos \frac { \pi } { 5 } \cos \frac { \pi } { 3 } - \sin \frac { \pi } { 5 } \sin \frac { \pi } { 3 }$ ​

Simplify the expression algebraically. $4 \tan \left( \frac { \pi } { 4 } - \theta \right)$ ​

Write the given expression as an algebraic expression. cos(arccos x - arcsin x)

A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system,the weight moves vertically from its equilibrium position,and this motion is modeled by​ $y = \frac { 1 } { 8 } \sin 2 t + \frac { 1 } { 6 } \cos 2 t$ where y is the distance from equilibrium (in feet)and t is the time (in seconds). Find the amplitude of the oscillations of the weight. ​

Write the given expression as the tangent of an angle. $\frac { \tan 3 x + \tan 4 x } { 1 - \tan 3 x \tan 4 x }$

Find the exact value of the given expression.​ $\cos \left( 300 ^ { \circ } + 135 ^ { \circ } \right)$

Simplify the following expression algebraically.​ $6 \tan ( \pi + \theta )$ ​

Find the expression as the sine or cosine of an angle.​ $\cos 9 x \cos 5 y + \sin 9 x \sin 5 y$ ​

Find the exact value of the given expression. $\cos \left( 120 ^ { \circ } + 315 ^ { \circ } \right)$

Use the formula $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \cos ( B \theta - C )$ ,where $C = \arctan ( a / b )$ $C = \arctan ( a / b ) , a > 0$ ,to rewrite the trigonometric expression in the form $a \sin B \theta + b \cos B \theta$ ​ 9 $\cos \left( \theta - \frac { \pi } { 4 } \right)$ ​

Find the expression as the sine of an angle.​ $\sin 5 \cos 1.7 - \cos 5 \sin 1.7$ ​

Simplify the expression algebraically. $5 \sin \left( \frac { \pi } { 6 } + x \right)$ ​

Simplify the following expression algebraically.​ $4 \sin \left( \frac { 3 \pi } { 2 } + \theta \right)$ ​

Find the exact value of $\sin ( u + v )$ given that $\sin u = \frac { 3 } { 5 }$ and $\cos v = - \frac { 24 } { 25 }$ .(Both u and v are in Quadrant II. )