Question

Draw a right-angled isosceles triangle with equal sides 1 cm. Use the triangle to find the exact values of cos 45° and sin 45°. What can you say about (cos 45°)2 + (sin 45°)2?

Answer 1

Answer:

Step-by-step explanation:

The 2 legs are both 1 cm long and the hypotenuse , by Pythagoras,

equals √(1^2 + 1^2) = √2.

The 2 angles other than the right angle are both 45 degrees.

sin 45 = opposite/hypotenuse =  1/√2

cos 45 = adjacent/hypotenuse = 1/√2

(cos 45°)^2 + (sin 45°)^2

= (1/√2)^2 + (1/√2)^2

= 1/2 + 1/2

= 1.