To figure this out you would have to multiply 40 by 2 since the first problem is 10 and the next is 20. So the answer would be 80.
If x terminates in the fourth quadrant, then we know that sin(x) < 0 and cos(x) > 0. Given that sec(x) = 8, we immediately have
cos(x) = 1/sec(x) = 1/8
Recall the Pythagorean identity,
cos²(x) + sin²(x) = 1
Then it follows that
sin(x) = -√(1 - cos²(x)) = -3√7/8
Now recall the double angle identities,
sin(2x) = 2 sin(x) cos(x)
cos(2x) = cos²(x) - sin²(x)
Then
sin(2x) = 2 (-3√7/8) (1/8) = -6√7/64 = -3√7/32
cos(2x) = (1/8)² - (-3√7/8)² = -62/64 = -31/32
By definition of tangent,
tan(x) = sin(x)/cos(x)
Then
tan(2x) = sin(2x)/cos(2x) = (=3√7/32) / (-31/32) = 3√7/31
To find the value of x, we can take the inverse sine of both sides. Let's do just that:
Note: This x is in radians. Your answer is
x = 0.3 rad or, depending on the instructions provided, it could be in degrees as
x = 15.47°.
Answer:
The remaining area of the circle is 196.06 cm².
Step-by-step explanation:
<em>(area of circle) - (area of triangle)</em><em> </em><em>=</em><em> </em><em>remaining</em><em> </em><em>area </em><em>of </em><em>the </em><em>circle</em>
<em>πr² - ½bh</em>
<em>3.14(8)² - ½(3)(4)</em>
<em>3.14(64) - ½(12)</em>
<em>202.06 - 6</em>
<em>= 196.06</em>