Question

if theta is an acute angle and 4 sin theta is equal to 3 find 4 sin square theta minus 3 cos square theta + 2....​

Answer 1

Answer:

47/16

Step-by-step explanation:

4sin theta= 3

sin theta= 3/4 = p/h

b= √ 16-9 = √7

cos theta= √7/4

4sin² theta- 3cos² theta +2 =

4×9/16 - 3×7/16 + 2 = 47/16

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Answer 2

Given: Θ is an acute angle and 4 sin Θ =3

To find: Value of $4 {sin}^{2} Θ - 3 {cos}^{2} Θ + 2$

Explanation: Let the perpendicular of the triangle be p, base be b and hypotenuse be h.

4 sin Θ= 3

=> sin Θ = 3/4

Now, sin Θ = p/h

Therefore, p = 3 and h= 4

To find base(b) of the triangle, the formula used is:

=>$b = \sqrt{ {h}^{2} - {p}^{2} }$

=>$b = \sqrt{ {4}^{2} - {3}^{2} }$

=>$b = \sqrt{16 - 9}$

=>$b = \sqrt{7}$

cos Θ= b/h

$cos \: Θ = \frac{ \sqrt{7} }{4}$

Now,

${sin}^{2} Θ = {( \frac{3}{4} )}^{2}$

${sin}^{2} Θ = \frac{9}{16}$

And,

${cos}^{2} Θ = { (\frac{ \sqrt{7} }{4} )}^{2}$

${cos}^{2} Θ = \frac{7}{16}$

Finding value of expression:

$4 {sin}^{2} Θ - 3 {cos}^{2} Θ + 2$

=$4 \times \frac{9}{16} - 3 \times \frac{7}{16} + 2$

=$\frac{36 - 21 + 32}{16}$

=$\frac{47}{16}$

Therefore, the value of the expression is 47/16.