Question 1

Use the formula for $\sin ( s - t )$ to compute the exact value of $\sin \frac { \pi } { 12 }$ .

Accepted Answer

A)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
B)  $\frac { \sqrt { 3 } - \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 3 } + \sqrt { 2 } } { 4 }$ 
D)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$ 
E)  $\frac { \sqrt { 3 } } { 4 }$ 
A)  $\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }$ 
B)  $\frac { \sqrt { 3 } - \sqrt { 2 } } { 4 }$ 
C)  $\frac { \sqrt { 3 } + \sqrt { 2 } } { 4 }$ 
D)  $\frac { \sqrt { 6 } - \sqrt { 2 } } { 4 }$ 
E)  $\frac { \sqrt { 3 } } { 4 }$

Question 2

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\cos \frac { 5 \pi } { 12 } \cos \frac { \pi } { 12 }$

Accepted Answer

A)  0 
B)  -1/4 
C)  -1/2 
D)  1/4 
E)  1/2 
A)  0 
B)  -1/4 
C)  -1/2 
D)  1/4 
E)  1/2

Question 3

Evaluate the quantity that is defined, but do not use a calculator or tables. $\arcsin \left( - \frac { 1 } { 2 } \right)$

Accepted Answer

A)  -π/4 
B)  -π/3 
C)  -π/2 
D)  π/4 
E)  -π/6 
A)  -π/4 
B)  -π/3 
C)  -π/2 
D)  π/4 
E)  -π/6

Question 4

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\sin 125 ^ { \circ } \sin 5 ^ { \circ }$

Accepted Answer

A)  $\frac { 1 } { 2 } \sin 130 ^ { \circ } - \frac { \sqrt { 3 } } { 4 }$ 
B)  $- \frac { 1 } { 4 } - \frac { 1 } { 2 } \cos 130 ^ { \circ }$ 
C)  $\frac { 1 } { 2 } \sin 130 ^ { \circ } + \frac { \sqrt { 3 } } { 4 }$ 
D)  $\sqrt { 3 } \cos 65 ^ { \circ }$ 
E)  $\frac { 1 } { 2 } \cos 130 ^ { \circ } - \frac { 1 } { 4 }$ 
A)  $\frac { 1 } { 2 } \sin 130 ^ { \circ } - \frac { \sqrt { 3 } } { 4 }$ 
B)  $- \frac { 1 } { 4 } - \frac { 1 } { 2 } \cos 130 ^ { \circ }$ 
C)  $\frac { 1 } { 2 } \sin 130 ^ { \circ } + \frac { \sqrt { 3 } } { 4 }$ 
D)  $\sqrt { 3 } \cos 65 ^ { \circ }$ 
E)  $\frac { 1 } { 2 } \cos 130 ^ { \circ } - \frac { 1 } { 4 }$

Question 5

Use the addition formulas for sine and cosine to simplify the expression. $$\sin 54 ^ { \circ } \cos 24 ^ { \circ } - \cos 54 ^ { \circ } \sin 24 ^ { \circ }$$

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  1/2 
C)  0 
D)  1 
E)  $\frac { \sqrt { 3 } } { 2 }$ 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  1/2 
C)  0 
D)  1 
E)  $\frac { \sqrt { 3 } } { 2 }$

Use the formula for $\sin ( s - t )$ to compute the exact value of $\sin \frac { \pi } { 12 }$ .

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\cos \frac { 5 \pi } { 12 } \cos \frac { \pi } { 12 }$

Evaluate the quantity that is defined, but do not use a calculator or tables. $\arcsin \left( - \frac { 1 } { 2 } \right)$

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\sin 125 ^ { \circ } \sin 5 ^ { \circ }$

Use the addition formulas for sine and cosine to simplify the expression. $\sin 54 ^ { \circ } \cos 24 ^ { \circ } - \cos 54 ^ { \circ } \sin 24 ^ { \circ }$

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 9: Analytical Trigonometry

Use the formula for sin⁡(s−t)\sin ( s - t )sin(s−t) to compute the exact value of sin⁡π12\sin \frac { \pi } { 12 }sin12π​ .

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. cos⁡5π12cos⁡π12\cos \frac { 5 \pi } { 12 } \cos \frac { \pi } { 12 }cos125π​cos12π​

Evaluate the quantity that is defined, but do not use a calculator or tables. arcsin⁡(−12)\arcsin \left( - \frac { 1 } { 2 } \right)arcsin(−21​)

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. sin⁡125∘sin⁡5∘\sin 125 ^ { \circ } \sin 5 ^ { \circ }sin125∘sin5∘

Use the addition formulas for sine and cosine to simplify the expression. sin⁡54∘cos⁡24∘−cos⁡54∘sin⁡24∘\sin 54 ^ { \circ } \cos 24 ^ { \circ } - \cos 54 ^ { \circ } \sin 24 ^ { \circ }sin54∘cos24∘−cos54∘sin24∘

Fundamentals

Equations and Inequalities

Functions

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Use the formula for $\sin ( s - t )$ to compute the exact value of $\sin \frac { \pi } { 12 }$ .

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\cos \frac { 5 \pi } { 12 } \cos \frac { \pi } { 12 }$

Evaluate the quantity that is defined, but do not use a calculator or tables. $\arcsin \left( - \frac { 1 } { 2 } \right)$

Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\sin 125 ^ { \circ } \sin 5 ^ { \circ }$

Use the addition formulas for sine and cosine to simplify the expression. $\sin 54 ^ { \circ } \cos 24 ^ { \circ } - \cos 54 ^ { \circ } \sin 24 ^ { \circ }$