Ontario 10 Applied (MFM2P)
topic badge
Find angles from sine, cosine and tangent measures
Lesson

As with every topic in mathematics, there is a conceptual side (what you need to know and understand) and a practical side (what you need to do and answer). To calculate values involving trigonometric expressions, it will often be easiest to use a scientific calculator.

Don't forget the three trigonometric ratios!

Trigonometric ratios

$\sin\theta=\frac{\text{Opposite }}{\text{Hypotenuse }}$sinθ=Opposite Hypotenuse

$\cos\theta=\frac{\text{Adjacent }}{\text{Hypotenuse }}$cosθ=Adjacent Hypotenuse

$\tan\theta=\frac{\text{Opposite }}{\text{Adjacent }}$tanθ=Opposite Adjacent

 

Worked example

Question 1

If $\sin\theta=0.65$sinθ=0.65, find $\theta$θ to the nearest degree.

Think: This question is asking us what the angle ($\theta$θ) is, if the ratio of the opposite side and hypotenuse is $0.65$0.65. To answer this question, we can use the inverse sine button on a calculator. It will probably look like $\sin^{-1}$sin1, and may involving pressing 'shift' or '2nd F'.

Do:

$\sin\theta$sinθ $=$= $0.65$0.65  
$\theta$θ $=$= $\sin^{-1}\left(0.65\right)$sin1(0.65) (Take the inverse sine)
$\theta$θ $=$= $40.54160187$40.54160187$\ldots$ (Evaluate with a calculator)
$\theta$θ $=$= $41$41 (Round to the nearest degree)

 

Practice questions

QUESTION 1

If $\cos\theta=0.146$cosθ=0.146, find $\theta$θ, writing your answer to the nearest degree.

QUESTION 2

If $\sin\theta=1$sinθ=1, find $\theta$θ.

QUESTION 3

If $\tan\theta=1.732$tanθ=1.732, find $\theta$θ, writing your answer to the nearest degree.

Outcomes

10P.MT2.02

Determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean Theorem

What is Mathspace

About Mathspace