For a right triangle with an angle θ : Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent. When we divide Sine by Cosine we get: So we can say: That is our first Trigonometric Identity.

For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse.

Enter a problem... Rewrite cot(x)⋅sin(x) cot (x) ⋅ sin (x) in terms of sines and cosines. Cancel the common factors. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

When the height and base side of the right triangle are known, we can find out the sine, cosine, tangent, secant, cosecant, and cotangent values using trigonometric formulas. The reciprocal trigonometric identities are also derived by using the trigonometric functions.

All the trigonometric identities are based on the six trigonometric ratios. They are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using the sides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side.

Basic trig identities are formulas for angle sums, differences, products, and quotients; and they let you find exact values for trig expressions.

These lessons, with video lessons, examples and step-by-step solutions, help Algebra 2 students to learn about the trigonometric function: Sin, Cos, Tan and the reciprocal trigonometric functions Csc, Sec and Cot.

How do you express #sin theta - cot^2 theta + tan^2 theta # in terms of #cos theta #?

sin(-x) = -sin(x) csc(-x) = -csc(x) cos(-x) = cos(x) sec(-x) = sec(x) tan(-x) = -tan(x) cot(-x) = -cot(x)

Answer- As evident from the name, quotient relations comprise three trigonometric ratios. In here, one is the quotient we get after division operation between the other two. For instance, tan θ = sin θ /cos θ and cot θ = cos θ / sin θ. Question- Who is the father of trigonometry?