Pregunta
Sketch an angle
in standard position such that
has the least possible positive measure, and the
point
is on the terminal side of
. Find the values of the six trigonometric functions for the
angle. Do not use a calculator.
point
angle. Do not use a calculator.
Ask by Edwards Pearson. in the United States
Jan 31,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The trigonometric functions for angle
are:
Solución
To find the trigonometric functions for the angle
in standard position with the point
on its terminal side, follow these steps:
-
Determine the Radius
: -
Compute the Trigonometric Functions:
-
Sine (
): -
Cosine (
): -
Tangent (
): -
Cosecant (
): -
Secant (
): -
Cotangent (
):
-
-
Summary of the Six Trigonometric Functions:
These values provide the exact trigonometric ratios for the angle
without using a calculator.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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The Deep Dive
To sketch the angle
in standard position, we start with the point
. This point is in the first quadrant since both coordinates are positive. We can draw the angle
from the positive x-axis to the line connecting the origin to the point.
Next, to find the values of the six trigonometric functions for the angle
, we need to first determine the length of the radius
, which is the distance from the origin to the point. This can be calculated using the Pythagorean theorem:
Now with
,
, and
, we can calculate the six trigonometric functions:
-
Sine:
-
Cosine:
-
Tangent:
-
Cosecant (the reciprocal of sine):
-
Secant (the reciprocal of cosine):
-
Cotangent (the reciprocal of tangent):
So, the final values of the six trigonometric functions are:
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