So I am new to sine, cosine, and tangent, so I need some help. Just explain it. No need for the answers unless you want to give it to me. :D
Let triangle ABC be a right triangle with angleC=90degrees. Given the tangent of one of the complementary angles of the triangle, find the tangent of the other angle.
tanA=1.25
tanB=1.50
tanC=1
To me, the easy way is to sketch the right triangle.
If TanA=1.25=5/4, then the tanB=4/5
if TanB=1.50=3/2, then the TanA=2/3
with the sketch, you can see the "opposite/adjacent" becomes the inverse.
On the last, I thought C was 90 deg. Tangent of 90deg is infinite.
To understand the concept of sine, cosine, and tangent, we first need to understand what a right triangle is and how it is defined.
A right triangle is a triangle that has one angle measuring 90 degrees (denoted by C in the given triangle ABC). The side opposite the right angle is called the hypotenuse (denoted by side c), while the other two sides are referred to as the legs (denoted by sides a and b).
Now, let's define the trigonometric functions sine, cosine, and tangent in the context of a right triangle:
- Sine (sin): The sine of an angle is defined as the ratio of the length of the side opposite that angle to the hypotenuse. In a right triangle ABC, sinA = a/c, sinB = b/c, and sinC = a/b.
- Cosine (cos): The cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse. In a right triangle ABC, cosA = b/c, cosB = a/c, and cosC = b/a.
- Tangent (tan): The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In a right triangle ABC, tanA = a/b, tanB = b/a, and tanC = a/b.
Given that angle C is 90 degrees, it means that angles A and B are complementary angles. The tangent of a complementary angle is equal to the reciprocal of the tangent of the other angle. In this case, if tanA = 1.25, then tanB will be the reciprocal of 1.25.
To find this, you can take the reciprocal of tanA:
tanB = 1/tanA = 1/1.25
Similarly, if you have the tangent of one angle, you can find the tangent of the other angle by taking the reciprocal.
Keep in mind that finding the reciprocal of a fraction involves flipping the numerator and denominator of the fraction.