Trigonometric Example Problems

Exact Value

100

arcsin-√2/2 = (?)

-π/4 or -45° 

200

cos^-11/2 = (?)

π/3 or 60°

300

arctan-√3 = (?)

-π/3 or -60°

400

sin^-13 = (?)

Undefined

500

sin(cos^-1x24/25) = (?)

7/25

Find Trig Values

100

Find the tan of (-7,2)

-2/7

200

Find the sec of cos = 5/8, where sin > 0

8/5

300

Find the sin of (4,3)

3/5

400

Find the csc of (-1,5)

√(26)/5

500

Find sin of cot = -3, where sin < 0

-√(10)/10

Graphs

100

Amplitude of 10sin(x+π)-1

10

200

Period of sin(x/2)

4π

300

Vertical shift of 18sin(x+π/4)+10

10

400

Phase shift of 15sin(x/2 - π/4)-10

π/2

500

Amplitude, period, phase shift, and vertical shift of 2sin(x+π/2)-3

Amp: 2

Period: 2π

P.S.: -π/2

V.S.: -3

Simplify

100

tan(x)csc(x)

sec(x)

200

tan(x)/sec(x)

sin(x)

300

sec²(x)cot(x)-cot(x)

tan(x)

400

csc²(x)cot²(x)+csc²(x)

csc⁴(x)

500

cos(x)(tan²(x) + 1)

sec(x)

Other

100

Find the reference angle of 330

30°

200

Pythagorean theorem

What is a² + b² = c²

300

Law of sines

What is sinA/a = sinB/b = sinC/c

400

sin(-x) = (?)

What is -sin(x)

500

cos(-x) = (?)

What is cos(x)