1.4:Trigonometric Functions

This section describes the relationship between radians and degrees. To convert from radians to degrees multiply the number by 180/pi, to convert the other way, from degrees to radians multiply by the reciprocal, pi/180. The section also explains how trigonometric functions are defined using right triangles. The Pythagorean Theorem is important to finding the values of the trigonometric functions in right triangles as well as in identities.

Problems:

#4. Convert from degrees to radians.

a) 1° =0.0175 radians

b) 30°=0.5236 radians

c) 25°=0.4363 radians

d) 120°=2.094 radians

To solve this problem I used my calculator and the formula for converting from degrees to radians. I multiplied each number in degrees by pi/180 to give the number of radians.

#38. Solve sinθ=cos 2θ for 0≤θ<2pi.

To solve this problem I substituted cos2θ for cos^2θ-sin^2θ, giving me sinθ= cos^2θ-sin^2θ. Then I set the whole equation to zero; sinθ -cos^2θ-sin^2θ=0. Using the double angle formulas, I changed the equation to sinθ-((1/2)*1 + cos2x) –((1/2)*1 – cos2x) = 0. Solving for sinθ, I found it to be equal to ½ and -1. On a unit circle, ½ corresponds to pi/6 and 5pi/6 and -1 corresponds to 3pi/2.