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5.2 Notes: Trig Ratios in Right Triangles
Ex. 1) Given a triangle below, find the values of sine, cosine, and tangent for
opp
hyp
adj
cos  
hyp
Reciprocal Trig Ratios
C
Trig Ratios
hyp
opp
hyp
sec  
adj
adj
cot  
opp
csc  
sin  
tan  
B.
13 in
12 in
opp
adj
A
x
B
Ex. 2) Given the triangle above, find the values of cosecant, secant, and cotangent for
Ex. 3) a.) If cos θ = 3 , find the sec θ.
4
c.) If tan θ = 15 , find the other five trig ratios.
17
B.
b.) If csc θ = 1.345, find sin θ.
Ex. 4) a.) Find the values of the six trigonometric
ratios for P.
b.) Find the values of the six trigonometric ratios
for R.
R
N
60 ̊
45 ̊
M
45 ̊
S
P
30 ̊
Confunctions:
If θ is an acute angle, sin θ = cos (90 ̊ - θ).
Similar relationships hold true for the other trigonometric ratios.
sin θ =
cos θ =
tan θ =
cot θ =
sec θ =
csc θ =
Ex. 5) If sec θ = 2.5, what is csc (90 ̊ - θ)?
Ex. 6) a.) cos (10 ̊ ) =
b.) tan (50 ̊ ) =
Ex. 7) a.) Find x: sin (x + 20 ̊ ) = cos (2x + 10 ̊ )
b.) Find x: tan (4x ̊ + 40 ̊ ) = cot (2x – 10 ̊ )
Q