4 sin^2 θ + 13cos^2 θ = 7
sin^2 θ = 1 - cos^ θ
4 - 4cos^2 θ + 13cos^2 θ = 7
9cos^2 θ = 3
cos^2 θ = 1/3
cos θ = # (1/3) # - square root
Square root of (1/3) has +1/3 and -1/3 as values of cos
Find the key angle by doing the cos inverse of #1/3
K.A = cos^-1 #(1/3) = 0.955
θ lies in all 4 quadrants
The values of θ are:
θ = 0.955, 2.186, 4.096, 7.23
Ignore 0.955, 2.186, 4.096, 7.23 as they are out of range pi/2 = 1.571
The the value of θ = 0.955 = 0.96 (to 2 d.p) radian
Hope it helped!
Answer:
no solution ...................
Answer:
Interior Angle: 165°
Exterior Angle: 15°
Step-by-step explanation:
So first you have to find the sum of all interior angles of a polygon with <u>24 sides</u>. This can be found using the formula:
sum = ( <em>n</em> - 2 ) * 180° where '<em>n</em>' is the number of sides.
When '<em>n</em> = 24' then the sum is:
sum = ( 24 - 2 ) * 180°
Simplify and solve.
sum = 22 * 180°
sum = 3960°
Since there are 24 sides to the polygon, there are 24 interior angles. <u>Assuming that this polygon is equilateral</u>, you can surmise that:
<em>Interior Angle</em> = sum° / <em>n</em> where n is the number of sides,
3960° / 24 = 165° = Interior Angle
Using that information, and combine it with the [Supplementary Angles Theorem] the exterior angle can be found by:
165° + x = 180°
Solve for x.
5x - 12y = 24 - it's a standard form of equation of a line
The slope-intercept form: y = mx + b
m - slope
b - y-intercept.
Convert the standard form to the slope-intercept form:
<em>subtract 5x from both sides</em>
<em>divide both sides by (-12)</em>

Answer: 