Download Sec 4.2 Notes (Trig Functions Acute Angles)

Name: _________________________________________ Date ___________________________________________ Pre-­‐Calculus Period:_____ Sec 4.2 Notes (Trig Functions of Acute Angles) Six Trigonometric Ratios opp
sin θ =
cscθ hyp
adj
cosθ =
secθ hyp
opp
tan θ =
cot θ adj
Ex 1 17
secθ = , find the remaining 5 trigonometric ratios. 5
45°-­‐45°-­‐90° Triangle Theorem In a 45°-­‐45°-­‐90° triangle, the hypotenuse is 2 times as long as each leg. Name: _________________________________________ Pre-­‐Calculus Date ___________________________________________ Period:_____ 30°-­‐60°-­‐90° In a 30°-­‐60°-­‐90° triangle, the hypotenuse is twice as long as the Triangle shorter leg, and the longer leg is 3 times as long as the shorter Theorem: leg. Use special triangles to fill in the following table 45˚ θ 30˚ sin(θ ) cos(θ ) tan(θ ) csc(θ ) sec(θ ) cot(θ ) 60˚ Name: _________________________________________ Date ___________________________________________ Ex 3 Use the table to evaluate (give exact values). Exact trig ratios with ⎛π⎞
tan ⎜ ⎟
radian ⎝ 4⎠
a) ⎛π⎞
cos ⎜ ⎟
⎝ 4⎠
b) Ex 4 Find angles when given ratios Solve for θ in degrees and radians 1
sin θ =
2 a) 2 3
b) cscθ =
3
Pre-­‐Calculus Period:_____ Name: _________________________________________ Pre-­‐Calculus Date ___________________________________________ Period:_____ Ex 5 A guy wire from the top of a transmission tower forms a 75˚ angle with the ground at a 55-­‐foot distance from the base of the tower. How tall is the tower?