If x is a positive acute angle and cos x = 3/5, find the value of sinx.
1 answer:
X is a positive acute angle. That means x is located in the first quadrant and has positive value in sin, cos, tan.
The formula of trigonometry ratio
cos x =
sin x =
From the formula of cosine
cos x =
from the formula above, adjacent side is 3 units, and hypotenuse is 5 units
Draw a right triangle to illustrate the location of the sides. See image attached.
To find the ratio of sine, we need to find the length of opposite side using pythagorean theorem
3² + (opposite)² = 5²
9 + (opposite)² = 25
(opposite)² = 25 - 9
(opposite)² = 16
opposite = 4
The length of opposite side is 4 units
Find sin x
sin x =
sin x =
The formula of trigonometry ratio
cos x =
sin x =
From the formula of cosine
cos x =
from the formula above, adjacent side is 3 units, and hypotenuse is 5 units
Draw a right triangle to illustrate the location of the sides. See image attached.
To find the ratio of sine, we need to find the length of opposite side using pythagorean theorem
3² + (opposite)² = 5²
9 + (opposite)² = 25
(opposite)² = 25 - 9
(opposite)² = 16
opposite = 4
The length of opposite side is 4 units
Find sin x
sin x =
sin x =
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Answer:
The function is increasing for all real values of x where
x < –4.
Step-by-step explanation:
we have
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex (h,k) represent a maximum
The roots of the function (or x-intercepts) are x=-6 and x=-2
The x-coordinate of the vertex is the midpoint of the roots
so
The y-coordinate of the vertex is
substitute the x-coordinate of the vertex in the quadratic equation
The vertex is the point (-4,4)
The function is increasing in the interval (-∞,-4)
The function is decreasing in the interval (-4,∞)