Math / Geometry

Question(a) Sketch $\theta=330^{\circ}$ in standard position.
Then sketch an angle between $-360^{\circ}$ and $0^{\circ}$ that is coterminal with $\theta$ .

Studdy Solution

STEP 1

What is this asking? We need to draw an angle of 330 degrees, and then draw a different angle that ends in the same spot, but is measured clockwise instead of counter-clockwise. Watch out! Remember coterminal angles land in the same spot, even if they're measured differently.
Don't get tripped up by the negative angle!

STEP 2

1. Draw the initial angle
2. Find the coterminal angle
3. Draw the coterminal angle

STEP 3

Remember, an angle in standard position has its vertex at the origin $(0, 0)$ and its initial side along the positive x-axis.
We measure counter-clockwise for positive angles.

STEP 4

Since a full circle is $360^\circ$ , an angle of $330^\circ$ is almost a full circle.
It's $360^\circ - 330^\circ = 30^\circ$ short of a full circle.
So, draw an angle that goes almost all the way around counter-clockwise, stopping $30^\circ$ short in the fourth quadrant.

STEP 5

Coterminal angles start and end at the same place, even if they are measured differently.
We're looking for a negative angle, which means we'll measure it clockwise.

STEP 6

We can find a coterminal angle by adding or subtracting multiples of $360^\circ$ .
Since we want a negative angle between $-360^\circ$ and $0^\circ$ , we need to measure clockwise.
Notice that $330^\circ$ is just $30^\circ$ short of a full circle in the counter-clockwise direction.
That means it's $-30^\circ$ in the clockwise direction!
So, our coterminal angle is $-30^\circ$ .

STEP 7

A negative angle means we measure clockwise from the positive x-axis.

STEP 8

Draw an angle that goes $30^\circ$ clockwise from the positive x-axis.
Notice how it ends in the exact same spot as the $330^\circ$ angle!

STEP 9

We've drawn the $330^\circ$ angle in standard position.
We've also drawn the $-30^\circ$ angle, which is coterminal with $330^\circ$ , meaning they both end at the same place.

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Question(a) Sketch $\theta=330^{\circ}$ in standard position.
Then sketch an angle between $-360^{\circ}$ and $0^{\circ}$ that is coterminal with $\theta$ .

Studdy Solution

STEP 1

STEP 2

1. Draw the initial angle
2. Find the coterminal angle
3. Draw the coterminal angle

STEP 3

Remember, an angle in standard position has its vertex at the origin $(0, 0)$ and its initial side along the positive x-axis.
We measure counter-clockwise for positive angles.

STEP 4

Since a full circle is $360^\circ$ , an angle of $330^\circ$ is almost a full circle.
It's $360^\circ - 330^\circ = 30^\circ$ short of a full circle.
So, draw an angle that goes almost all the way around counter-clockwise, stopping $30^\circ$ short in the fourth quadrant.

STEP 5

Coterminal angles start and end at the same place, even if they are measured differently.
We're looking for a negative angle, which means we'll measure it clockwise.

STEP 6

STEP 7

A negative angle means we measure clockwise from the positive x-axis.

STEP 8

Draw an angle that goes $30^\circ$ clockwise from the positive x-axis.
Notice how it ends in the exact same spot as the $330^\circ$ angle!

STEP 9

We've drawn the $330^\circ$ angle in standard position.
We've also drawn the $-30^\circ$ angle, which is coterminal with $330^\circ$ , meaning they both end at the same place.

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Question(a) Sketch θ=330∘\theta=330^{\circ}θ=330∘ in standard position.Then sketch an angle between −360∘-360^{\circ}−360∘ and 0∘0^{\circ}0∘ that is coterminal with θ\thetaθ.

Studdy Solution

STEP 1

STEP 2

1. Draw the initial angle2. Find the coterminal angle3. Draw the coterminal angle

STEP 3

Remember, an angle in **standard position** has its vertex at the origin (0,0)(0, 0)(0,0) and its initial side along the positive x-axis.We measure counter-clockwise for positive angles.

STEP 4

STEP 5

**Coterminal angles** start and end at the same place, even if they are measured differently.We're looking for a *negative* angle, which means we'll measure it *clockwise*.

STEP 6

STEP 7

A negative angle means we measure *clockwise* from the positive x-axis.

STEP 8

Draw an angle that goes 30∘30^\circ30∘ *clockwise* from the positive x-axis.Notice how it ends in the *exact same spot* as the 330∘330^\circ330∘ angle!

STEP 9

We've drawn the 330∘330^\circ330∘ angle in standard position.We've also drawn the −30∘-30^\circ−30∘ angle, which is coterminal with 330∘330^\circ330∘, meaning they both end at the same place.

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Question(a) Sketch $\theta=330^{\circ}$ in standard position.
Then sketch an angle between $-360^{\circ}$ and $0^{\circ}$ that is coterminal with $\theta$ .

1. Draw the initial angle
2. Find the coterminal angle
3. Draw the coterminal angle

Remember, an angle in standard position has its vertex at the origin $(0, 0)$ and its initial side along the positive x-axis.
We measure counter-clockwise for positive angles.

Coterminal angles start and end at the same place, even if they are measured differently.
We're looking for a negative angle, which means we'll measure it clockwise.

A negative angle means we measure clockwise from the positive x-axis.

Draw an angle that goes $30^\circ$ clockwise from the positive x-axis.
Notice how it ends in the exact same spot as the $330^\circ$ angle!

We've drawn the $330^\circ$ angle in standard position.
We've also drawn the $-30^\circ$ angle, which is coterminal with $330^\circ$ , meaning they both end at the same place.