Question

Find the value of the six trig functions given the triangle below.

Answer 1

To find the values of the six trigonometric functions, we need to determine the lengths of the sides of the triangle.

We can then use the definitions of the trigonometric functions to find the values.

In order to find the values of the six trigonometric functions, we need to determine the lengths of the sides of the triangle. Let's assume the triangle is a right triangle with one angle measuring 90 degrees.

We can then use the definitions of the trigonometric functions to find the values:

• Sine (sin): The sine of an angle is equal to the ratio of the length of the opposite side to the hypotenuse.
• Cosine (cos): The cosine of an angle is equal to the ratio of the length of the adjacent side to the hypotenuse.
• Tangent (tan): The tangent of an angle is equal to the ratio of the length of the opposite side to the adjacent side.
• Cosecant (csc): The cosecant of an angle is equal to the reciprocal of the sine.
• Secant (sec): The secant of an angle is equal to the reciprocal of the cosine.
• Cotangent (cot): The cotangent of an angle is equal to the reciprocal of the tangent.

Answer 2

`\text{Here,}\\\\\text{Opposite side,}~ O = 2\\\\\text{Hypotenuse,}~ H = \sqrt 5 \\\\\text{Adjacent side,}~ A = √(5-4) = \sqrt 1 =1 ~~ ;[\text{By using Pythagorean theorem}]\\\\\\\sin \theta = \frac{O}H = \frac 2{\sqrt 5}\\\\\\\cos \theta = (A)/(H) = (1)/(\sqrt 5) \\ \\\\ \tan \theta = (O)/(A) = \frac 21 = 2`

`csc \theta = (1)/(\sin \theta) = \frac{\sqrt 5}2\\\\\\\sec \theta = (1)/(\cos \theta) = \sqrt 5 \\\\\\\cot \theta = \frac 1{\tan \theta} = \frac 12`