GCSE Maths Practice: trigonometry

Question 3 of 10

This question introduces finding angles using cosine with inverse functions.

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\( \begin{array}{l}\text{Find } \theta \text{ if } \cos \theta = \frac{1}{2}.\end{array} \)

Choose one option:

Label sides carefully, and check calculator is in degree mode.

Cosine relates the adjacent side and hypotenuse in a right-angled triangle: \(\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\). To find an angle when cosine is known, use the inverse cosine function \(\theta = \cos^{-1} (value)\). For \(\cos \theta = 1/2\), \(\theta = 60^\circ\). Remember that in the first quadrant, angles range 0°–90°, which is the range for GCSE right-angled triangles. Practice using the inverse cosine with different triangle sizes and sides. Ensure your calculator is in degree mode to avoid errors. Understanding inverse trig functions allows you to find missing angles in applied problems like ramps, towers, and distances.

Visualize the triangle and identify adjacent and hypotenuse sides before applying \(\cos^{-1}\). Practice helps reinforce concepts and increases accuracy.