While sine and cosine are readily identifiable as the projections of the radius on the vertical and horizontal axis, we need to see the definition of the tangent to understand how to find it and visualize it: \tan (\alpha) = \frac {\sin (\alpha)} {\cos (\alpha)} tan(α) = cos(α)sin(α) \(\sin{x} = \frac{o}{h}\), \(\cos{x} = \frac{a}{h}\) and \(\tan{x} = \frac{o}{a}\) Or: \(s^o_h~c^a_h~t^o_a\). Accurate trigonometric ratios for 0°, 30°, 45°, 60° and 90° Learn how to find sin cos tan values for any angle using formulas, table and examples. Find out the trigonometric ratios of sine, cosine, tangent, cotangent, secant and cosecant for different angles. See how to use the formulas and the chart to solve problems involving sin cos tan values.
Learn the basic and Pythagorean identities for trigonometric functions, such as sin, cos, tan, cot, sec and csc. Find out how to use them to simplify expressions, calculate angles and solve equations. See examples, formulas and diagrams.
Learn how to calculate sine, cosine and tangent of any angle using a right-angled triangle. See examples, formulas, graphs and exercises to practice the functions. Find out the difference between sine, cosine and tangent, and the other functions such as secant, cosecant and cotangent. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side. They are often written as sin (x), cos (x), and tan (x), where x is an angle in radians or degrees. Created by Sal Khan. Solving for an angle in a right triangle using the trigonometric ratios Sine and cosine of complementary angles Modeling with right triangles The reciprocal trigonometric ratios Unit 2: Trigonometric functions 0/1900 Mastery points
Basic Identities: tan( tan( cot( sin( ) ) = cos( ) ) = cot( ) ) = tan( ) cot( sec( csc( Pythagorean Identities cos2( ) + sin2( ) = 1 sec2( ) − tan2( ) = 1 ) ) cos( = sin( ) ) = 1 cos( ) ) = sin( ) csc2( ) − cot2( ) = 1 Double Angle Identities sin(2 ) = 2 sin( ) cos( ) cos(2 ) = 1 − 2 sin2( ) cos(2 ) = 2 cos2( ) − 1 cos(2 tan(2
Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.
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    • sin cos tan rules