3. Find the size of the angle $$ heta $$ where $$ heta $$ is acute. $$ \begin{array}{ll} ext { a. } \sin heta=0.529 & ext { c. } an heta=1.8 \ ext { b. } \cos heta=0.493 & ext { d. } \cos heta=0.5\end{array} $$

Question

3. Find the size of the angle $$ 	heta $$ where $$ 	heta $$ is acute. $$ \begin{array}{ll}	ext { a. } \sin 	heta=0.529 & 	ext { c. } 	an 	heta=1.8 \ 	ext { b. } \cos 	heta=0.493 & 	ext { d. } \cos 	heta=0.5\end{array} $$

UpStudy AI · Accepted Answer

To find the size of the angle $$ 	heta $$ where $$ 	heta $$ is acute, we can use the inverse trigonometric functions.

Given:
a. $$ \sin 	heta = 0.529 $$
b. $$ \cos 	heta = 0.493 $$
c. $$ 	an 	heta = 1.8 $$
d. $$ \cos 	heta = 0.5 $$

We can use the inverse sine, inverse cosine, and inverse tangent functions to find the angle $$ 	heta $$ in each case.

Let's calculate the angle $$ 	heta $$ for each given trigonometric function:
Calculate the value by following steps:
- step0: Calculate:
  $$\arcsin\left(0.529ight)$$
Calculate or simplify the expression $$ \arcsin(0.493) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\arcsin\left(0.493ight)$$
Calculate or simplify the expression $$ \arctan(1.8) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\arctan\left(1.8ight)$$
Calculate or simplify the expression $$ \arccos(0.5) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\arccos\left(0.5ight)$$
- step1: Calculate the trigonometric value:
  $$\frac{\pi }{3}$$
The size of the angle $$ 	heta $$ where $$ 	heta $$ is acute for each given trigonometric function is as follows:

a. $$ 	heta \approx 0.557422 $$ radians
b. $$ 	heta \approx 0.515535 $$ radians
c. $$ 	heta \approx 1.063698 $$ radians
d. $$ 	heta \approx 1.047198 $$ radians

Therefore, the size of the angle $$ 	heta $$ where $$ 	heta $$ is acute for each given trigonometric function is approximately the values calculated above.
The angles $$ 	heta $$ for the given trigonometric functions are approximately: a. $$ 	heta \approx 0.557 $$ radians b. $$ 	heta \approx 0.516 $$ radians c. $$ 	heta \approx 1.064 $$ radians d. $$ 	heta \approx 1.047 $$ radians

3. Find the size of the angle \( \theta \) where \( \theta \) is acute. \( \begin{array}{ll}\text { a. } \sin \theta=0.529 & \text { c. } \tan \theta=1.8 \\ \text { b. } \cos \theta=0.493 & \text { d. } \cos \theta=0.5\end{array} \)

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