Given a trigonometric identity, verify that it is true. Work on one side of the equation. It is usually better to start with the more complex side, as it is easier to simplify than to build. Similarly, we will prove other reciprocal identities. cos θ = Base/Hypotenuse = b/a and cosec θ = Hypotenuse/Base = a/b ⇒ cos θ is the reciprocal of sec θ and sec θ is the reciprocal of cos θ. tan θ = sin θ/cos θ and cot θ = cos θ/sin θ ⇒ tan θ is the reciprocal of cot θ and cot θ is the reciprocal of tan θ. Hence, we have
If you look up trigonometric identities on Google you will find a bunch of ways to transform sine, cosine, and tangent into one another as well as their reciprocal functions. The basics are this: (sin (x)) 2 + (cos (x)) 2 = 1. tan (x) = sin (x) / cos (x) With those two equations, you can transform a combination of the functions in so many
The tangent function in terms of the sine function can be written as, tan θ = sin θ/(√1 – sin 2 θ) We know that, tan θ = sin θ/cos θ. From the Pythagorean identities, we have, sin 2 θ + cos 2 θ = 1. cos 2 θ = 1 – sin 2 θ. cos θ = √(1 – sin 2 θ) Hence, tan θ = sin θ/(√1 – sin 2 θ) Tangent Function in Terms of the
Sine and Cosine of Complementary Angles. Recall that the sine and cosine of angles are ratios of pairs of sides in right triangles.. The sine of an angle in a right triangle is the ratio of the side opposite the angle to the hypotenuse.
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what is cos tan sin