Draw a picture and show all work.
Given sinA=4/5 and cosA<0, find tanA
To find the value of tan(A), we can use the trigonometric identity:
tan(A) = sin(A) / cos(A)
We are given that sin(A) = 4/5 and cos(A) < 0.
First, let's draw a right triangle to represent the given information.
Let the angle A be inside the triangle. The side opposite to angle A is the vertical side, and the side adjacent to angle A is the horizontal side.
Next, label the sides of the triangle:
Opposite side (vertical side) = 4
Hypotenuse (the longest side) = 5
Based on the given information, cos(A) is negative, which means the horizontal side should be negative.
Now, let's use the Pythagorean theorem to find the adjacent side:
(a^2) + (b^2) = (c^2)
(4^2) + (b^2) = (5^2)
16 + (b^2) = 25
b^2 = 25 - 16
b^2 = 9
b = 3
So, the adjacent side (horizontal side) is -3.
Now, we can substitute the values into the trigonometric identity:
tan(A) = sin(A) / cos(A)
tan(A) = (4/5) / (-3)
Therefore, the value of tan(A) is -4/15.