Question

Find the values of all 6 trigonometric functions for the angle inside right triangle where the opposite side of the angle is 9 cm and hypothenuse of the triangle is 13 cm.

Answer 1

Answer:

• See below

Step-by-step explanation:

Find the missing leg x first using Pythagorean:

• $x=\sqrt{13^2-9^2} =\sqrt{169-81} =\sqrt{88}$

Now the 6 functions, considering angle α opposite to leg with length of 9:

sine = opposite/hypotenuse

• sin α = 9 / 13

cosine = adjacent/hypotenuse

• cos α = √88 / 13

tangent = opposite / adjacent

• tan α = 9 / √88

cotangent = adjacent / opposite

• cot α = √88 / 9

secant = hypotenuse / adjacent

• sec α = 13 / √88

cosecant = hypotenuse / opposite

• csc α = 13 / 9

Answer 2

• P=9cm
• H=13cm

B=

$\\ \sf\longmapsto \sqrt{13^2-9^2}=\sqrt{169-81}=\sqrt{88}\approx9.5$

Now

$\\ \sf\longmapsto sinA=\dfrac{P}{H}=\dfrac{9}{13}$

$\\ \sf\longmapsto cosA=\dfrac{B}{H}=\dfrac{9.5}{13}$

$\\ \sf\longmapsto tanA=\dfrac{P}{B}=\dfrac{9}{9.5}$

$\\ \sf\longmapsto cotA=\dfrac{1}{tanA}=\dfrac{9.5}{9}$

$\\ \sf\longmapsto secA=\dfrac{1}{cosA}=\dfrac{13}{9.5}$

$\\ \sf\longmapsto cosecA=\dfrac{1}{sinA}=\dfrac{13}{9}$