Trigonometric Ratios
The six trigonometric ratios are: sine, cosine, tangent, secant, cosecant, and cotangent. Sine and cosecant are inverse ratios. Cosine and secant are inverse ratios. Tangent and cotangent are also inverse ratios. The relationships among these ratios are contained in Trigonometry. Trigonometry refers to the branch of Mathematics that tackles the angles and sides of any roght triangle.
Learning Task 2:
Answers:
1. hypotenuse = 8
sin 30° = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex] csc 30° = [tex]\frac{8}{4}[/tex] = 2
cos 30° = [tex]\frac{4\sqrt{3} }{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] sec 30° = [tex]\frac{2}{\sqrt{3} }[/tex] = [tex]\frac{2\sqrt{3} }{3}[/tex]
tan 30° = [tex]\frac{4}{4\sqrt{3} }[/tex] = 1[tex]\sqrt{3}[/tex] cot 30° = [tex]\frac{4\sqrt{3} }{4}[/tex] = [tex]\sqrt{3}[/tex]
2. opposite/adjacent = 3
sin 45° = [tex]\frac{3}{3\sqrt{2} }[/tex] = 1[tex]\sqrt{2}[/tex] csc 45° = [tex]\frac{3\sqrt{2} }{3}[/tex] = [tex]\sqrt{2}[/tex]
cos 45° = [tex]\frac{3}{3\sqrt{2} }[/tex] = 1[tex]\sqrt{2}[/tex] sec 45° = [tex]\frac{3\sqrt{2} }{3}[/tex] = [tex]\sqrt{2}[/tex]
tan 45° = [tex]\frac{3}{3}[/tex] = 1 cot 45° = [tex]\frac{3}{3}[/tex] = 1
Solutions:
1. Given: opposite side - 4 inches
adjacent side - 4[tex]\sqrt{3}[/tex] inches
hypotenuse - ?
Solutions: hypotenuse² = opposite² + adjacent²
hypotenuse² = (4 inches)² + (4[tex]\sqrt{3}[/tex] inches)²
hypotenuse² = 16 + 16(3)
hypotenuse² = 16 + 48
hypotenuse² = 64
[tex]\sqrt{hypotenuse^2}[/tex] = [tex]\sqrt{64}[/tex]
hypotenuse = 8
then,
sin 30° = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex] csc 30° = [tex]\frac{8}{4}[/tex] = 2
cos 30° = [tex]\frac{4\sqrt{3} }{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] sec 30° = [tex]\frac{2}{\sqrt{3} }[/tex] = [tex]\frac{2\sqrt{3} }{3}[/tex]
tan 30° = [tex]\frac{4}{4\sqrt{3} }[/tex] = 1[tex]\sqrt{3}[/tex] cot 30° = [tex]\frac{4\sqrt{3} }{4}[/tex] = [tex]\sqrt{3}[/tex]
2. Given: opposite side - ?
adjacent side - ?
hypotenuse side - 3[tex]\sqrt{2}[/tex]
opposite side = adjacent side
Solutions: hypotenuse² = opposite² + adjacent²
opposite² = hypotenuse² - adjacent²
opposite² = (3[tex]\sqrt{2}[/tex])² - opposite² ( since opposite = adjacent)
opposite² = 9(2) - opposite²
opposite² + opposite² = 18
2 opposite² = 18
2 2
opposite² = 9
[tex]\sqrt{opposite^2}[/tex] = [tex]\sqrt{9}[/tex]
opposite = 3
adjacent = 3 (since opposite and adjacent sides are equal)
then,
sin 45° = [tex]\frac{3}{3\sqrt{2} }[/tex] = 1[tex]\sqrt{2}[/tex] csc 45° = [tex]\frac{3\sqrt{2} }{3}[/tex] = [tex]\sqrt{2}[/tex]
cos 45° = [tex]\frac{3}{3\sqrt{2} }[/tex] = 1[tex]\sqrt{2}[/tex] sec 45° = [tex]\frac{3\sqrt{2} }{3}[/tex] = [tex]\sqrt{2}[/tex]
tan 45° = [tex]\frac{3}{3}[/tex] = 1 cot 45° = [tex]\frac{3}{3}[/tex] = 1
What are the six trigonometric ratios: https://brainly.ph/question/527509
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