3.7 Evaluating Trig Functions

Ex 1) Find the value (round to 4 dec. places) To properly evaluate trig ratios on our calculator, we need to make sure we are in the right MODE – Degrees or Radians If it has a degree symbol  put in Degree Mode If no symbol at all  put in Radian Mode Ex 1) Find the value (round to 4 dec. places) a) cos 275° (degree mode) cos 275° = 0.0872 b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511 c) tan 2 (radian mode) tan 2 = –2.1850

Ex 2) Find the value (round to 4 dec. places) To evaluate ratios when given Deg-Min-Sec, either convert to just degrees or use the °, ʹ, ʺ buttons on your calculator To evaluate csc x, sec x & cot x, you will need to utilize the fact that they are reciprocal functions Remember: Ex 2) Find the value (round to 4 dec. places) a) sec 146° (degree mode) OR b) cot 39° 52ʹ 15ʺ (degree mode)

We can also solve for an angle (in degrees or radians) if we know the ratio. Use the inverse trig functions (sin–1, cos–1, tan–1) *Often these problems can have more than 1 answer – you need to think and draw a sketch!! Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to nearest tenth) (degree mode!!) a) sin θ = 0.7193 θ θ θ = sin–1(0.7193) θ = 46.0° AND… sinθ is (+) in QI & QII 180 – 46 = 134.0° θ = 46.0° and 134.0°

Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to nearest tenth) (degree mode!!) b) tan θ = –0.2309 θ = tan–1(–0.2309) θ = –13.0° 13.0° –13.0° tanθ is (–) in QIV & QII 180 – 13 = 167.0° 360 – 13 = 347.0° θ = 167.0° and 347.0°

Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest hundredth) (radian mode!!) a) cos θ = –0.4611 θ = cos–1(–0.4611) θ = 2.05 2.05 –2.05 cosθ is (–) in QII & QIII 2π – 2.05 = 4.23 θ = 2.05 rad and 4.23 rad

Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest hundredth) (radian mode!!) b) sec θ = 8.2986 1.45 –1.45 cosθ is (+) in QI & QIV 2π – 1.45 = 4.83 θ = 1.45 rad and 4.83 rad