What Is Negative Cosine Equal To?

What does negative cosine mean?

When a point (a,b) is reflected in the x-axis, it moves to the point (a,-b).

So Q also has coordinates (cos(θ),-sin(θ)).

Therefore: cos(-θ) = cos θ & sin(-θ) = – sin θ.

These are the negative angle identities..

Can hypotenuse be negative?

Because it is the length of the side of a triangle and lengths cannot be negative.

What is the reciprocal of sin?

The cosecant is the reciprocal of the sine. The secant is the reciprocal of the cosine. The cotangent is the reciprocal of the tangent.

What does a negative cosine graph look like?

Hare – sign is in front of the cosine graph. If we draw the negative cosine it will produce the reflection about the x – axis. So the negative cosine graph will be opposite to the positive graph.

What is trigonometry formula?

Basic Formulas By using a right-angled triangle as a reference, the trigonometric functions or identities are derived: sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side. sec θ = Hypotenuse/Adjacent Side.

Why is negative cosine positive?

Now the measure of the angle is -m, a negative value when measured clockwise is, because all angles have to be acute to apply the various trigonometrical ratios or relations. Hence, cosine of a negative angle changes into a positive value.

What is cos equivalent to?

The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp). (1) Memorize: sine = (opposite side) / hypotenuse. cosine = (adjacent side) / hypotenuse.

Is the hypotenuse always the longest side?

The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg a, substitute the known values into the Pythagorean Theorem.

How do you convert COS to sin?

For example, cosθ = sin (90° – θ) means that if θ is equal to 25 degrees, then cos 25° = sin (90° – 25°) = sin 65°.

What are the six trigonometric functions?

There are six main trigonometric functions:Sine (sin)Cosine (cos)Tangent (tan)Secant (sec)Cosecant (csc)Cotangent (cot)

What Quadrant is sec negative?

Quadrant IIIIn Quadrant III, cot ⁡ θ \displaystyle \cot{\theta} cotθ is positive, csc ⁡ θ \displaystyle \csc{\theta} cscθ and sec ⁡ θ \displaystyle \sec{\theta} secθ are negative.

Is Quadrant 4 positive or negative?

In Quadrant I, both the x– and y-coordinates are positive; in Quadrant II, the x-coordinate is negative, but the y-coordinate is positive; in Quadrant III both are negative; and in Quadrant IV, x is positive but y is negative.

Can cosine be negative?

As a result, sine will be positive, but cosine will be negative, and all tangent values will be negative.) In the third quadrant, all x and y values will be negative, so all sine and cosine values will be negative. Tangent will be positive because a negative divided by a negative is positive.)

What happens when sine is negative?

Both x and y coordinates are negative in the third quadrant. Since the hypotenuse is a +1, both the sine and the cosine must be negative. As the angle increases from 180° to 270°, the sine increases in magnitude but is now negative, so, the sine decreases from 0 to -1.

Where is sin cos and tan negative?

For an angle in the second quadrant the point P has negative x coordinate and positive y coordinate. Therefore: In Quadrant II, cos(θ) < 0, sin(θ) > 0 and tan(θ) < 0 (Sine positive). For an angle in the third quadrant the point P has negative x and y coordinates.

Is sin even or odd?

Sine is an odd function, and cosine is an even function. You may not have come across these adjectives “odd” and “even” when applied to functions, but it’s important to know them. A function f is said to be an odd function if for any number x, f(–x) = –f(x).

How do you prove sin 45?

In a right triangle, one angle is, by definition, 90 degrees so the two acute angles sum to 180- 90= 90 degrees. To prove that sin(45 (degrees)) is 1√2 , consider that if a right triangle has one angle with measure 45 degrees then the other acute angle is 90- 45= 45 degrees also.

Why is sin 30 the same as SIN 150?

it’s because the reference angle for 150 is equal to 30. that reference angle is the angle within the triangle formed from dropping a perpendicular to the x-axis of the unit circle. … the internal angle of the triangle in quadrant 2 is equal to 180 – 150 which is equal to 30 degrees. that is called the reference angle.