Question

please help........
what is the range of 5sinx-12cosx+7??????
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Answer 1

Step-by-step explanation:

This may help you buddy..

Answer 2

Answer- The above question is from the chapter 'Trigonometric functions'.

Trigonometry- The branch of Mathematics which helps in dealing with measure of three sides of a right-angled triangle is called Trigonometry.

Trigonometric Ratios:

sin θ  = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

cosec θ = Hypotenuse/Perpendicular

sec θ = Hypotenuse/Base

cot θ = Base/Perpendicular

Also, tan θ = sin θ/cos θ and cot θ = cos θ/sinθ

Concept used: Range of a sin x + b cos x is

$[- \sqrt{a^{2} \: + \: b^{2}} \: , \: \sqrt{a^{2} \: + \: b^{2}}\: ]$

Given question: What is the range of 5 sin x - 12 cos x + 7?

Solution: Let y = 5 sin x - 12 cos x

a = 5

b = -12

Range of y is as follows:-

$- \sqrt{a^{2} \: + \: b^{2}} \leq y \leq \sqrt{a^{2} \: + \: b^{2}}\\\\-\sqrt{5^{2} \: + \: (-12)^{2}} \leq y \leq \sqrt{5^{2} \: + \: (-12)^{2}}\\\\- \sqrt{25 +144} \leq y \leq \sqrt{25 + 144}\\\\-\sqrt{169} \leq y \leq \sqrt{169}\\\\-13 \leq y \leq 13$

y + 7 = 5 sin x - 12 cos x + 7

$-13 + 7 \leq 5 \: sin \: x - 12 \: cos \: x + 7 \leq 13 + 7\\\\-6 \leq 5 \: sin \: x - 12 \: cos \: x + 7 \leq 20$

∴ Range of 5 sinx - 12 cosx + 7 = [-6 , 20].