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Example Questions
Example Question #2932 : Act Math
For triangle , what is the cotangent of angle
?
The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is
Example Question #22 : Tangent
What is the tangent of the angle formed between the origin and the point if that angle is formed with one side of the angle beginning on the
-axis and then rotating counter-clockwise to
? Round to the nearest hundredth.
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the -axis as your reference point for your angle. (Hence, it is called the "reference angle.")
Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:
So, the tangent of an angle is:
or, for your data,
.
This is . Rounding, this is
. Since
is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.
Example Question #2933 : Act Math
What is the tangent of the angle formed between the origin and the point if that angle is formed with one side of the angle beginning on the
-axis and then rotating counter-clockwise to
? Round to the nearest hundredth.
Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the -axis as your reference point for your angle. (Hence, it is called the "reference angle.")
Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:
So, the tangent of an angle is:
or, for your data,
, or
. Since
is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.
Example Question #22 : Trigonometry
A ramp is being built at an angle of from the ground. It must cover
horizontal feet. What is the length of the ramp? Round to the nearest hundredth of a foot.
Based on our information, we can draw this little triangle:
Since we know that the tangent of an angle is , we can say:
This can be solved using your calculator:
or
Now, to solve for , use the Pythagorean Theorem,
, where
and
are the legs of a triangle and
is the triangle's hypotenuse. Here,
, so we can substitute that in and rearrange the equation to solve for
:
Substituting in the known values:
, or approximately
. Rounding, this is
.
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