If sin theta=24 divide by 25 and theta is acute..make use of a diagram to determine the value of 7(tanø-secø)
recognize that we have a 7-24-25 triangle, so if
sinθ = 24/25,
cosθ = 7/25
tanθ = 24/7
now plug in the needed values
To determine the value of 7(tanø - secø), where sin θ = 24/25 and θ is acute, we can use a right triangle diagram.
1. Start by drawing a right triangle. Label the angle opposite to the side with length 24 and the hypotenuse with length 25. Since sin θ = 24/25 and θ is acute, the opposite side is 24, and the hypotenuse is 25.
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24 | \ 25
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2. Next, use the Pythagorean theorem to find the length of the remaining side, which we can label as "x". The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, we have:
x^2 + 24^2 = 25^2
Simplifying this equation, we get:
x^2 + 576 = 625
Subtract 576 from both sides:
x^2 = 625 - 576
x^2 = 49
Taking the square root of both sides, we find:
x = 7
Therefore, the length of the remaining side is 7.
3. Now, let's find the value of tan θ. Tan θ is equal to the ratio of the opposite side to the adjacent side. So:
tan θ = opposite / adjacent = 24 / 7
4. Next, let's find the value of sec θ. Sec θ is equal to the ratio of the hypotenuse to the adjacent side. So:
sec θ = hypotenuse / adjacent = 25 / 7
5. Finally, substitute the values of tan θ and sec θ into the expression 7(tan ø - sec ø):
7(tan ø - sec ø) = 7(24/7 - 25/7) = 7(-1/7) = -1
Therefore, the value of 7(tan ø - sec ø) is -1.