# Compound Angle Identity (Trigonometry)Activity Part 1 (Sine)

## Investigate Compound Angle Identities

There are two right-angled triangles named as PSQ and RSQ with marked angles. Angle PQS is denoted by A ( black shaded angle) and Angle SPQ = 90-A ( Yellow shaded). Angle RQS is denoted by B ( turquoise shaded angle) & Angle SRQ= 90-B ( brown shaded)

## Compound Angles

You may use slider now to move point R, try to visualize how the whole angle PQR is changing. And choose the correct options for the following questions. 1. if P and R are on the opposite side of S then Angle PQR = 2. If P and R are on the right-hand side of S then Angle PQR = ( for this you need to use slide me)

Select all that apply
• A
• B
• C

## Work out the lengths of sides of each triangle.

1.Triangle PQS, side PQ = y and Angle PQS= A. Determine sides PS and QS in terms of y and angle A 2. Triangle RQS, side RQ = x and Angle RQS= B. Determine sides RS and QS in terms of x and angle B

## Did you get two different expressions for QS

Two different expressions or same expressions for QS

Select all that apply
• A
• B

## Ask the teacher for print copy and complete all the working steps or follow the link

Link for file: https://drive.google.com/file/d/1oyUaOBoddmy9mdhqmbK-_PQif3_n8amR/view?usp=sharing Task 1: Apply the sine rule: in the triangle, PQR to obtain an expression for sin(A+B), after working out on the page enter your result here

## Use Slide me and move point R such that you see the angle A-B

Then Repeat all steps ( as you did in sin(A+B) case) for sin(A-B). After working out on a printed copy provided (from the link) enter your result here