In Exercises 63–68, find the exact value of each expression. Do not use a calculator. cos 12° sin 78° + cos 78° sin 12°

Find the remaining five trigonometric functions of θ.

sin θ = -4/5, cos θ < 0

Find the remaining five trigonometric functions of θ.

cos θ = -1/4, sin θ > 0

Concept Check Does there exist an angle θ with the function values cos θ = ⅔ and sin θ = ¾?

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. csc 37° sec 53° - tan 53° cot 37°

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos 40° = 2 cos 20°

Use the even-odd identities to evaluate the expression.

$\(\cos\]\left\)(-\(\theta\[\right\))-\(\cos\]\theta\)$

Use the even-odd identities to evaluate the expression.

$-\(\cot\]\left\)(\(\theta\[\right\))\(\cdot\]\sin\[\left\)(-\(\theta\]\right\))$

Select the expression with the same value as the given expression.

$\(\sec\[\left\)(-\(\frac{4\pi}{5}\]\right\))$