Finding The Values Of The Other Five Trig Functions When Give In six trigonometric ratios sin, cos, tan, csc, sec and cot, if the value of one of the ratios is given, we can find the values of the other five functions. the following steps will be useful in the above process. step 1 : the given given trigonometric ratio has to compared with one of the formulas given below. sin θ = opposite side hypotenuse. Use the tangent identity to find tan θ tan θ. tan θ = sin θ cos θ = 4 5 3 5 = 4 3 tan θ = sin θ cos θ = 4 5 3 5 = 4 3. find the other three trigonometric functions of θ θ from #1. to find secant, cosecant, and cotangent use the reciprocal identities. csc θ = 1 sin θ = 1 4 5 = 5 4 sec θ = 1 cos θ = 1 3 5 = 5 3 cot θ = 1 tan θ = 1.
Given A Trig Function Find The Other 5 Youtube The other trigonometric functions find exact values of the trigonometric functions secant, cosecant, tangent, and cotangent to define the remaining functions, we will once again draw a unit circle with a point [latex]\left(x,y\right)[ latex] corresponding to an angle of [latex]t[ latex], as shown in figure 1. The trigonometric functions are periodic. for the four trigonometric functions, sine, cosine, cosecant and secant, a revolution of one circle, or 2π, will result in the same outputs for these functions. and for tangent and cotangent, only a half a revolution will result in the same outputs. Example 5.4.2 find trigonometric functions given one trig ratio and the quadrant the angle is in. given sec(θ) = 2√6 3 with θ in quadrant iv. find the value of sinθ and cotθ. solution. step 1. angle θ is in qiv where x> 0 and y <0. step 2. sec(θ) = 2√6 3 = r x, therefore we can choose r = 2√6 and x = 3. Finding exact values of the trigonometric functions secant, cosecant, tangent, and cotangent to define the remaining functions, we will once again draw a unit circle with a point ( x , y ) ( x , y ) corresponding to an angle of t , t , as shown in figure 1 .
The Other Five Trigonometric Functions Given One Youtube Example 5.4.2 find trigonometric functions given one trig ratio and the quadrant the angle is in. given sec(θ) = 2√6 3 with θ in quadrant iv. find the value of sinθ and cotθ. solution. step 1. angle θ is in qiv where x> 0 and y <0. step 2. sec(θ) = 2√6 3 = r x, therefore we can choose r = 2√6 and x = 3. Finding exact values of the trigonometric functions secant, cosecant, tangent, and cotangent to define the remaining functions, we will once again draw a unit circle with a point ( x , y ) ( x , y ) corresponding to an angle of t , t , as shown in figure 1 . Find the values of the other five trigonometric functions. example 2. tan θ = − 5 12, π 2 < θ < π. first, we know that θ is in the second quadrant, making sine positive and cosine negative. for this problem, we will use the pythagorean identity 1 tan 2 θ = sec 2 θ to find secant. 1 (− 5 12) 2 = sec 2 θ 1 25 144 = sec 2 θ 169. The cotangent function is the reciprocal of the tangent function. in figure 7.4.1 7.4. 1, the cotangent of angle t t is equal to cos t sin t = x y, y ≠ 0. cos. . t sin. . t = x y, y ≠ 0. the cotangent function is abbreviated as cot. cot. the cosecant function is the reciprocal of the sine function.
How To Find The Exact Value Of Five Remaining Trig Functions Givenо Find the values of the other five trigonometric functions. example 2. tan θ = − 5 12, π 2 < θ < π. first, we know that θ is in the second quadrant, making sine positive and cosine negative. for this problem, we will use the pythagorean identity 1 tan 2 θ = sec 2 θ to find secant. 1 (− 5 12) 2 = sec 2 θ 1 25 144 = sec 2 θ 169. The cotangent function is the reciprocal of the tangent function. in figure 7.4.1 7.4. 1, the cotangent of angle t t is equal to cos t sin t = x y, y ≠ 0. cos. . t sin. . t = x y, y ≠ 0. the cotangent function is abbreviated as cot. cot. the cosecant function is the reciprocal of the sine function.
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