01 February 2022 Trigonometric ratios for special angles
01 February 2022 Trigonometric ratios for special angles. www. mathssupport. org
Look at this isosceles right-angled triangle. A We let the equal sides have length 1. 1 Using Pythagoras’ theorem, the 3 rd side is c c 2 = 12 + 12 c 2 = 2 C 1 www. mathssupport. org B
Now look at the trigonometric ratios for this triangle Take any angle, say B. A Label the sides h o opposite hypotenuse C adjacent hypotenuse 1 1 a B opposite adjacent www. mathssupport. org
Look at this equilateral triangle. Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length. B 2 A Let the sides be 2 cm. 2 1 1 2 C You will see why 2 is a convenient length. Divide the triangle into 2 equal right angled triangles. We will take only one triangle to work www. mathssupport. org
Now look at this right-angled triangle, which is half the equilateral triangle. B Using Pythagoras’ theorem, the 3 rd side is 2 A a 1 www. mathssupport. org 22 = a 2 + 12 a 2 = 22 - 12 a 2 = 3
Now look at the trigonometric ratios for this triangle B Label the sides for this angle h 2 o A a 1 opposite hypotenuse adjacent hypotenuse opposite adjacent www. mathssupport. org
Now look at the trigonometric ratios for this triangle B Label the sides for this angle h 2 a A o 1 opposite hypotenuse adjacent hypotenuse opposite adjacent www. mathssupport. org
Trigonometric ratios for special Summary angles 0 sin cos tan On top of cosine the angles write down the numbers - 4 sine Write for thethe same but in inverse order For tangent, divide value ofand sine by cosine Square root the number on values top divide by 20 for www. mathssupport. org
Trigonometric ratios for three SOH CAH special angles TOA Find the exact value of x in this triangle First label the sides We are given the side adjacent to the angle and we want to find the length of the opposite side, so we use: opposite adjacent tan θ = h a o x 5 m www. mathssupport. org x 5
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