Practice Trigonometry
Sine, cosine and tangent relate angles to side-length ratios in right-angled triangles.
Identify the hypotenuse and the sides relative to the chosen angle first.
Exercises with solutions
In a right-angled triangle: sin α = opposite ÷ hypotenuse, cos α = adjacent ÷ hypotenuse and tan α = opposite ÷ adjacent. The leg next to the angle α is the adjacent side; the one across from it is the opposite side. Check that your calculator is set to degrees before calculating.
Exercise 1
The opposite side is 3 cm and the hypotenuse 5 cm. Calculate sin α.
Show solution and working
0.6
sin α = opposite ÷ hypotenuse = 3 cm ÷ 5 cm = 0.6.
Exercise 2
The adjacent side is 4 cm and the hypotenuse 5 cm. Calculate cos α.
Show solution and working
0.8
cos α = adjacent ÷ hypotenuse = 4 cm ÷ 5 cm = 0.8.
Exercise 3
The opposite side is 3 cm and the adjacent side 4 cm. Calculate tan α.
Show solution and working
0.75
tan α = opposite ÷ adjacent = 3 cm ÷ 4 cm = 0.75.
Exercise 4
What does sin² α + cos² α always equal?
Show solution and working
1
This follows from Pythagoras’ theorem. Check with the 3-4-5 triangle: 0.6² + 0.8² = 0.36 + 0.64 = 1.
Common mistake
Swapping opposite and adjacent. Which leg is which depends on the angle you look at: for the other acute angle they swap roles. And leaving the calculator in radians although the angle is given in degrees.
Keep learning with MatheJump
Create a free account and explore math practice. Choose from the available exercises to suit your learning needs.