Download 5 1practice solutions (1)

NAME _____________________________________________ DATE ____________________________ PERIOD _____________
5-1 Practice
Trigonometric Identities
Find the value of each expression using the given information.
1
1. If cos θ = 4 and 0˚ < θ < 90˚, find tan θ.
2. If sin θ =
3
and 0˚ < θ < 90˚, find cos θ.
√𝟓
√𝟏𝟓
3. If tan θ =
2
𝟑
7
2
and 0˚ < θ < 90˚, find sin θ.
4. If tan θ = 2 and 0˚ < θ < 90˚, find cot θ.
𝟕√𝟓𝟑
𝟏
𝟓𝟑
𝟐
4
𝟒
𝟓
𝟑
𝟑
5. If sin α = – 5 and cos α > 0, find tan α and sec α. tan α = – , sec α =
3
6. If cot x = – 2 and sec x < 0, find sin x and cos x. sin x =
𝟐√𝟏𝟑
𝟏𝟑
, cos x = –
𝟑√𝟏𝟑
𝟏𝟑
𝜋
7. If cos θ = 0.54, find sin (𝜃 − ). –0.54
2
𝜋
8. If cot x = –0.18, find tan (𝑥 − 2 ). 0.18
Simplify each expression.
9. cos x + sin x tan x sec x
11. sin2 θ cos2 θ – cos2 θ –𝐜𝐨𝐬 𝟒 θ
cot 𝐴
10. tan 𝐴
12.
–𝐜𝐨𝐭 𝟐 A
csc2 𝑥 − cot2 𝑥
sin (−𝑥) cot 𝑥
–sec x
13. KITE FLYING Brett and Tara are flying a kite. When the string is tied to the ground, the height of the kite can be
𝐿
determined by the formula 𝐻 = csc θ, where L is the length of the string and θ is the angle between the string and the
level ground. What formula could Brett and Tara use to find the height of the kite if they know the value of sin θ?
H = L sin θ
Chapter 5
7
Glencoe Precalculus