Compound Angle Identity (Trigonometry)Activity Part 1 (Sine)
Investigate Compound Angle Identities
Investigate Compound Angle Identities
There are two right-angled triangles named as PSQ and RSQ with marked angles.[br]Angle PQS is denoted by A ( black shaded angle) and Angle SPQ = 90-A ( Yellow shaded).[br]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.[br]1. if P and R are on the opposite side of S then Angle PQR =[br]2. If P and R are on the right-hand side of S then Angle PQR = ( for this you need to use slide me)
Work out the lengths of sides of each triangle.
1.Triangle PQS, side PQ = y and Angle PQS= A.[br]Determine sides PS and QS in terms of y and angle A [br][br]2. Triangle RQS, side RQ = x and Angle RQS= B.[br]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
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[br][br]Task 1:[br]Apply the sine rule:[math]\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}=\frac{sin\left(C\right)}{c}[/math][br]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).[br]After working out on a printed copy provided (from the link) enter your result here
Print this copy for students