Question

What are two angles within 0°-360° that has a cosine of negative root three over 2? Show work please




Determine two angles between 0° and 360° that has a cosine of this number without the use of a calculator

Answer 1

Answer:

150° and 210°

Step-by-step explanation:

1) according to the condition the required cosine is <0, it means the required angles are in the II-d and III-d quaters (see the attached picture no. 1);

2) it is known, that arccos(√3/2)=30°- the angle is between 0° and 90°, - but the requred angles are between 90° and 270° (see the picture no. 2), then

3) (angle)₁=180°-arccos(√3/2) and (angle)₂=180°+arccos(√3/2), then finally

(angle)₁=180°-30°=150°; (angle)₂=180°+30°=210°.

PS. note, the suggested way is not the only one.