4.2 Trig Functions of Acute Angles

Trig Functions Adjacent Opposite Hypotenuse A B C Sine (θ) = sin = Cosine (θ ) = cos = Tangent (θ) = tan = Cosecant (θ) = csc = Secant (θ ) = sec = Cotangent (θ) = cot = θ Acute Angle

Find the values of all six trig functions for an angle of 45° sin 45°= cos 45°= tan 45° = csc 45°= sec 45°= cot 45° = 45° 1 1

Find the values of all six trig functions for an angle of 30° Sin 30°= Cos 30°= Tan 30° = Csc 30°= Sec 30°= Cot 30° = 30° 1 2 √3

You Try! Find the values of all six trig functions for an angle of 60° Sin 60°= Cos 60°= Tan 60° = Csc 60°= Sec 60°= Cot 60° =

Find the values of all six trig functions of the angle θ Sin θ= Cos θ= Tan θ= Csc θ= Sec θ= Cot θ= 7 11 θ

You Try! Let be an acute angle such that sin θ = 3/7. Evaluate the remaining trig functions. Sin θ= 3/7 Cos θ= Tan θ= Csc θ= Sec θ= Cot θ=

Save yourself the frustration! Degree Mode vs. Radian Mode

Evaluate using a calculator (Find exact value, not an approximation) sec 45° csc

sin 74° cot You Try! Evaluate using a calculator (round answer to 3 decimal places)

Solving a right triangle 15 x 34°

A tree casts a shadow 532 ft long. Find the height of the tree if the angle of elevation of the sun is 25.7°

Homework Read “Common Calculator Errors” pg Pg : 6, 12, 16, 26, 28, 30, 40, 54, 62