Find the value of (7)/(3 × 2) + 1/6

Question

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Step 1: Given sin A = 12/13, use the identity sin² A + cos² A = 1. sin² A + cos² A = 1; Step 2: Substitute sin A = 12/13. cos² A = 1 − ( 12/13 )² Step 3: Compute ( 12/13 )². ( 12/13 )² = 144/169 Step 4: Simplify. cos² A = 1 − 144/169 = 169/169 − 144/169 = 25/169 Step 5: Solve for cos A. cos A = ± √(25/169) = ± 5/13; Assuming acute angle, cos A = 5/13. 5/13 Step 1: Given cos B = 3/5, use the identity sin² B + cos² B = 1. sin² B + cos² B = 1; Step 2: Substitute cos B = 3/5. sin² B = 1 − ( 3/5 )² Step 3: Compute ( 3/5 )². ( 3/5 )² = 9/25 Step 4: Simplify. sin² B = 1 − 9/25 = 25/25 − 9/25 = 16/25 Step 5: Solve for sin B. sin B = ± √(16/25) = ± 4/5; Assuming acute angle, sin B = 4/5. 4/5

Find the value of (7)/(3 × 2) + (1)/(6)

Answer

Step-by-step solution

Given $\sin A = \frac{12}{13}$ , use the identity $\sin^2 A + \cos^2 A = 1$ .

Substitute $\sin A = \frac{12}{13}$ .

Compute $\left( \frac{12}{13} \right)^2$ .

Simplify.

Solve for $\cos A$ .

Given $\cos B = \frac{3}{5}$ , use the identity $\sin^2 B + \cos^2 B = 1$ .

Substitute $\cos B = \frac{3}{5}$ .

Compute $\left( \frac{3}{5} \right)^2$ .

Simplify.

Solve for $\sin B$ .

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Find the value of (7)/(3 × 2) + (1)/(6)

Answer

Step-by-step solution

Given sin⁡A=1213\sin A = \frac{12}{13}sinA=1312​, use the identity sin⁡2A+cos⁡2A=1\sin^2 A + \cos^2 A = 1sin2A+cos2A=1.

Substitute sin⁡A=1213\sin A = \frac{12}{13}sinA=1312​.

Compute (1213)2\left( \frac{12}{13} \right)^2(1312​)2.

Simplify.

Solve for cos⁡A\cos AcosA.

Given cos⁡B=35\cos B = \frac{3}{5}cosB=53​, use the identity sin⁡2B+cos⁡2B=1\sin^2 B + \cos^2 B = 1sin2B+cos2B=1.

Substitute cos⁡B=35\cos B = \frac{3}{5}cosB=53​.

Compute (35)2\left( \frac{3}{5} \right)^2(53​)2.

Simplify.

Solve for sin⁡B\sin BsinB.

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More Mathematics Questions

Given $\sin A = \frac{12}{13}$ , use the identity $\sin^2 A + \cos^2 A = 1$ .

Substitute $\sin A = \frac{12}{13}$ .

Compute $\left( \frac{12}{13} \right)^2$ .

Solve for $\cos A$ .

Given $\cos B = \frac{3}{5}$ , use the identity $\sin^2 B + \cos^2 B = 1$ .

Substitute $\cos B = \frac{3}{5}$ .

Compute $\left( \frac{3}{5} \right)^2$ .

Solve for $\sin B$ .