I. Intro to Trig
(a.) Determine the quadrant in which the terminal side of the angle lies. (b.) Determine
two coterminal angles (one positive and one negative) for the given angle.
1.) 160°
2.) 5.5
3.) −
11𝜋
4.)
4
2𝜋
5
State the quadrant in which 𝜃 lies.
5.) 𝑠𝑖𝑛𝜃 < 0, 𝑐𝑜𝑠𝜃 < 0
6.) 𝑠𝑖𝑛𝜃 > 0, 𝑐𝑜𝑠𝜃 > 0
7.) 𝑠𝑖𝑛𝜃 > 0, 𝑡𝑎𝑛𝜃 < 0
8.) 𝑠𝑒𝑐𝜃 > 0, 𝑐𝑜𝑡𝜃 < 0
9.) 𝑐𝑜𝑡𝜃 > 0, 𝑐𝑜𝑠𝜃 > 0
10.) 𝑡𝑎𝑛𝜃 > 0, 𝑐𝑠𝑐𝜃 < 0
Find the exact value of each.
3
11.) If 𝑐𝑜𝑠𝜃 = 5 and 𝑠𝑖𝑛𝜃 < 0, find 𝑐𝑠𝑐𝜃.
12.) If 𝑡𝑎𝑛𝜃 = −
12
5
and 𝑠𝑖𝑛𝜃 > 0, find 𝑠𝑖𝑛𝜃.
Find the reference angle, 𝜃′, for the given angle.
13.) −95°
14.) 5.5
15.)
7𝜋
8
II. Trig Graphs and Inverses
(a.) Name a, b, c, d, and the associated transformations for each. (b.) Find the amplitude
and period. (c.) Find the domain and range.
𝑥
1.) 𝑦 = −2 sin (2 − 𝜋) + 1
2.) 𝑦 = −3 cos(2𝑥 + 𝜋) − 5
Find the exact value.
3.) arccos⁡(𝑐𝑜𝑠
5𝜋
4
6.) sin⁡(𝑎𝑟𝑐𝑡𝑎𝑛1)
)
4.) arctan⁡(𝑡𝑎𝑛0)
7.) sin⁡(𝑎𝑟𝑐𝑐𝑜𝑠
√3
)
2
5.) arccos⁡(𝑐𝑜𝑠
3𝜋
2
)