Exam 6: Trigonometric Identities and Conditional Equations

For the given function, determine the amplitude and find the phase shift. -y = -4 sin x -3 cos x Give the phase shift in radians rounded to the nearest thousandth.

Simplify the expression by using a sum or difference identity. -sin (59°) cos(41°) + sin(-31°) sin(-41°)

Simplify the expression by using a sum or difference identity. -sin (20°) cos (-70°) - cos (20°) sin (-70°)

Determine whether the function is odd, even, or neither. -f(t) = tan t + cos t

Find all real numbers in the interval that satisfy the equation. -cot 2t + 1 = csc 2t

Use an identity to write the expression as a single trigonometric function or as a single number. -

Find all real numbers in the interval that satisfy the equation. -tan x + sec x = 1

Find all real numbers in the interval that satisfy the equation. -sin x = 1 - 2 s

Use a product-to-sum identity to rewrite the expression. -sin 19° sin 31°

Graph the function by first writing it in the form y = A sin(x + C). State the amplitude, period, and phase shift. -y = cos x + 4 sin x

Find the exact value of the expression using the provided information. -Find tan(A - B) with A in quadrant II, and sin , with B in quadrant II.

Solve the problem. -A block is attached to a spring and set into motion. For this block and spring, the location on the surface at any time t seconds is given in meters by x = sin t + cos t. Find the maximum distance reached by the block from The resting position.

Factor and, if possible, simplify the expression. -

Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. - + 5 tan x + 3 = 0

Solve the equation. -

Identify the equation as either an identity or not. - = 2 cos 2x

Use a half-angle identity to find an exact value for the following, given the information about x. -Find cos , given that sin and 360° < x < 450°.

Find all angles in degrees that satisfy the equation. Round approximate answers to the nearest tenth of a degree. -cos

For the following equation, graph on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -

Choose the expression with exactly the same value as the given expression. -sin(107°)