# Evaluate the sine cosine and tangent of the following angles.

Using your calculator with only acute angles, evaluate the sine, cosine and tangent of each of the following angles, correct to 3 sig. fig.

(a) 276.1 (b) 135.7

Would someone mind explaining the two following examples? I'm not sure I should be using the CAST system (draw a graph to plot)/ how to fully evaluate angle.

• I'm assuming these angles are in degrees. Neither is an acute angle, but they will make acute angles to one of the coordinates axes. The problem appears to be asking you to find the trig values associated with those acute angles and then turn them into appropriate values (inserting or not inserting a minus sign) for the given angles. So you will probably find making a graph or similar diagram helpful. – colormegone Apr 1 '14 at 19:19
• Thank you, would you mind doing a diagram for one so I know the formula to follow? – user136213 Apr 1 '14 at 19:46

## 1 Answer

Each of the angles makes an acute angle to one of the coordinate axes, even though the full angle runs into some quadrant of the unit circle other than the first quadrant. You will want to work out what that acute angle (between 0º and 90º) is for each of the given angles, find the trig values for them from a calculator, then assign the appropriate sign (positive or negative) to each of those trig values.

Here is a graph of the angles: • So we know in the 4th quadrant you minus from 360, meaning 360-276.1 = 83.9. As we're asked to find the sin it would be -83.9. Is that all I have to find out? Or is there more? – user136213 Apr 1 '14 at 20:32
• Why don't I just do sin276.1 and then inverse? Could I do that in all cases (for cos and tan). – user136213 Apr 1 '14 at 20:36
• You don't want inverses; you are just being asked for sine, cosine, and tangent values. Yes, you could just input the given angles and ask for the trig values, but the question asks you to use angles between 0º and 90º in order to find results, so you will have to show that in your work in some way. – colormegone Apr 1 '14 at 21:44
• Would 92.4 be sin = 87.6, cos - =87.6 and tan = 87.6? And would 239 be sin = -59, cos = -59 and tan = 59? Is that the correct way to answer? – user136213 Apr 1 '14 at 22:42
• If you had the angle 92.4º, it makes an angle of 87.6º above the negative $\ x-$ axis; so $\ \sin 92.4º \ = \ \sin 87.6º \ , \ \cos 92.4º \ = \ -(\cos 87.6º) \ ,$ and $\tan 92.4º \ = \ -(\tan 87.6º) \ .$ You would find the trig values for 87.6º on a calculator and use those as shown here. For 239º, which makes a 59º angle below the negative $\ x-$ axis, you have $\ \sin 239º \ = \ -(\sin 59º) \ , \ \cos 239º \ = \ -(\cos 59º) \ ,$ and $\tan 239º \ = \ \tan 59º \ .$ (Now that I'm clearer about what you're asking, I think you mostly have it sorted out.) – colormegone Apr 1 '14 at 22:49