 ## Question

secondary 3 | A Maths

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##### Nicole She

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Pls help me with this question. Thank you

Date Posted: 3 months ago
Views: 22
Eric Nicholas K
3 months ago
For this type of question, we are not allowed to write out the actual value of the angle A. We can use it for checking answers though.

Since cos A = 1/2, it means that cos A has a positive value. From this information alone, we can identify that A lies in the first quadrant or the fourth quadrant.

Since sin A has the same sign as cos A, sin A has a positive value. From this information, we can identify that A lies in the first quadrant or the second quadrant.

Since A refers to the same angle, A must be in the first quadrant.

We proceed to draw a right angle triangle in the first quadrant starting at the origin and touching the x-axis. In other words, you should be drawing a diagonal line from the origin in the first quadrant to a certain point and then draw a line vertically downwards from that point.

Now, the angle touching the x-axis inside the triangle which is not 90 degrees is angle A. Since cos A = 1/2 and we know very well that cos is adj/hyp, we can set the adj length to 1 and the hyp length to 2. Solving for the opp length gives sqrt 3.

We see from here that sin A = (sqrt 3) / 2 and tan A = sqrt 3.

From here, we can proceed to solve the next part.

Since A lies in the first quadrant, -A lies in the fourth quadrant and sin in the fourth quadrant is negative,

sin (-A) = - sin A = - (sqrt 3) / 2

(the negative sign in front of sin A reflects the fact that sin in the fourth quadrant is the negative of the sin in the first quadrant). 