The trigonometric functions are defined based on the ratios of two sides of the right triangle. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. These functions are often abbreviated as sin, cos, tan, csc, sec, and cot. Their definitions are shown below. cos (θ + θ) = cos θ cos θ − sin θ sin θ cos (2 θ) = cos 2 θ − sin 2 θ cos (θ + θ) = cos θ cos θ − sin θ sin θ cos (2 θ) = cos 2 θ − sin 2 θ Using the Pythagorean properties, we can expand this double-angle formula for cosine and get two more interpretations. Using tan x = sin x / cos x to help. If you can remember the graphs of the sine and cosine functions, you can use the identity above (that you need to learn anyway!) to make sure you get your asymptotes and x-intercepts in the right places when graphing the tangent function. At x = 0 degrees, sin x = 0 and cos x = 1. Tan x must be 0 (0 / 1) Multiplying both sides times 40, you're going to get, let's see. 40 divided by 30 is 4/3. 4/3 sine of 40 degrees is equal to sine of theta, is equal to sine of theta. Now to solve for theta, we just need to take the inverse sine of both sides. So inverse sine of 4 over 3 sine of 40 degrees. Let us use the sin cos formula cos 2 θ + sin 2 θ = 1. Rewriting, we get cos 2 θ = 1 - sin 2 θ = 1-(9/25) cos 2 θ = 16/25. cos θ = 4/5. sin2θ = 2 sin θ cos θ = 2 × (3/5) × (4/5) = 24/25. Answer: sin2θ = 24/25. Example 3: Prov e (cos 4a - cos 2a)/ (sin 4a + sin 2a) = -tan a. Solution: Using the sin cos formula, let us rewrite the LHS 1 in 100 is 0.01, and tan(0.01) is approximately 0.01 radians We also know that 1 radian is about 57 degrees, so 0.01 radians is about 0.57 degrees Also the cosine function gets close to 1 for small radian values. The six trigonometric functions are called sine, cosine, tangent, cosecant, secant, and cotangent. Their domain consists of real numbers, but they only have practical purposes when these real numbers are angle measures. Consider an angle θ in standard position. Take a point P anywhere on the terminal side of the angle. The sine of Θ, noted as sin(Θ), represents the ratio the side opposite divided by the hypotenuse (i.e. sin(Θ) = a/c). The cosine of Θ, written as cos(Θ), is the side adjacent divided by the hypotenuse (i.e. cos(Θ) = b/c). The tangent of Θ, simply known as tan(Θ), is the side opposite divided by the side adjacent (i.e. tan(Θ) = a/b a year ago. If you think about it in terms of a right triangle, you can have angles and opposite sides, let C be the right angle and c be the hypotenuse. Then you have angle A and side opposite a and angle B and side opposite b. The sin (A)=opp/hyp ]=a/c and the cos (A)=adj/hyp=b/c. Also, the sin (B)=b/c and cos (B)=a/c. The circle looks like this: Fig 6. Unit circle showing sin (45) = cos (45) = 1 / √2. As a result of the numerator being the same as the denominator, tan (45) = 1. Finally, the general reference Unit Circle. It reflects both positive and negative values for X and Y axes and shows important values you should remember. LcmcOyx.