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compound angle formula. Suppose that you have two angles: Angle A and Angle B . Then we can prove that sin ( A + B ) = sin A cos B + cos A sin B. compound angle formula.

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compound angle formula

Suppose that you have two angles: Angle A and Angle B. Then we can prove that sin(A + B) = sinAcosB + cosAsinB


compound angle formula

Suppose that you have two angles: Angle A and Angle B. Then we can prove that sin(A + B) = sinAcosB + cosAsinB

i.e. sin(A + B) will be calculated on the right angle triangle


compound angle formula

1. By using right-angled triangle OSR, in which the length OS equals 1, determine the length of OR in terms of angle B.

then rearrange

hypotenuse

adjacent


compound angle formula

hypotenuse

adjacent

2. By using the answer of part 1 and right angle triangle ORQ determine the length ofQR in terms of angles A andB.

LengthOR was calculated from the cosine ratio, you knew the adjacent and the hypotenuse.

Labelling the right-angle triangle OQR

OQ

QR

OR

Adjacent

Opposite

Hypotenuse


compound angle formula

4. What is the angle TRO?

What sort of angle is this?


compound angle formula

4. What is the angle TRO? 5.What is the angle TRS? 6.What is the angle RST?

180 – 90 – (90 – A) = A

A

This is 90-A degrees.

90-A

A

This is A, so as the triangle is right-angled the other part of the angle is 90 – A.

This is 90 degrees.


compound angle formula

7. By using right angled triangle OSR determine the length of RS.

Use sine because we want to find out the opposite and we know the opposite.

calculation

Hypotenuse

Opposite

Adjacent


compound angle formula

8. By using the answer of part 7 and right angled triangle RST determine the length of TS.

A

Adjacent

Hypotenuse


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