if 8 tan Q=15 then sinA-cosA=?
or tan Q = 15/8
make a diagram, and
in quadrant I
sin Q = 15/17 and cosQ = 8/17
you now have sinA - cosA
I hope you meant
sinQ - cosQ
= 15/17 - 8/17 = 7/17
in quadrant III
sinQ = -15/17 and cosQ = -8/17
sinQ - cosQ = -15/17 + 8/17 = -7/17
To find the value of sinA - cosA, we need more information. The given equation 8 tan Q = 15 involves the tangent function, but we require the values of sinA and cosA to determine sinA - cosA.
To solve this problem, we need to find the values of sinA and cosA separately. Here's how you can do it:
1. Start with the equation 8 tan Q = 15:
Divide both sides by 8: tan Q = 15/8.
2. Recall that the tangent function is defined as tan Q = sinQ / cosQ.
So, we can rewrite the equation as sinQ / cosQ = 15/8.
3. Now, let's use the trigonometric identity: sin^2Q + cos^2Q = 1.
Multiply both sides of our equation by cos^2Q:
sinQ = (15/8)cosQ.
4. Substitute sinQ = (15/8)cosQ into the identity sin^2Q + cos^2Q = 1:
(15/8)^2cos^2Q + cos^2Q = 1.
5. Simplify the equation:
(225/64)cos^2Q + cos^2Q = 1.
Multiply both sides by 64 to eliminate the fraction:
225cos^2Q + 64cos^2Q = 64.
6. Combine like terms:
(225 + 64)cos^2Q = 64.
289cos^2Q = 64.
cos^2Q = 64/289.
7. Take the square root of both sides to find cosQ:
cosQ = ±√(64/289).
Since the cosine function is positive in the first and fourth quadrant, cosQ = √(64/289).
8. Finally, we can find sinA using the equation sinQ = (15/8)cosQ:
sinQ = (15/8) * √(64/289).
Multiply the fractions:
sinQ = (15√64) / (8√289).
Simplify the square roots:
sinQ = (15 * 8) / (8 * 17).
sinQ = 15/17.
Now that we have the values of sinQ and cosQ, we can calculate sinA - cosA:
sinA - cosA = sinQ - cosQ = (15/17) - √(64/289).