Table of Contents
Welcome to cos -45°, our post aboutthe cosine of -45 degrees.
For the cos minus 45 degrees we use the abbreviation cos for the trigonometric function together with the degree symbol °, and write it as cos -45°.
If you have been looking for what is cos -45°, or if you have been wondering about cos -45 degrees in radians, then you are right here, too.
In this post you can find the cos -45° value, along with identities.
Read on to learn all about the cos of -45°.
Cos Minus 45 Degrees
If you want to know what is cos -45 degrees in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of cos -45°:
cos -45° = √(2)/2
cos -45 degrees = √(2)/2
The cos of -45 degrees is √(2)/2, the same as cos of -45 degrees in radians. To obtain -45 degrees in radian multiply -45° by $\pi$ / 180° = -1/4 $\pi$. Cos -45degrees = cos (-1/4 × $\pi)$.
Our results of cos-45° have been rounded to five decimal places. If you want cosine -45° with higher accuracy, then use the calculator below; our tool displays ten decimal places.
To calculate cos -45 degrees insert the angle -45 in the field labelled °, but if you want to calculate cos -45 in radians, then you have to press the swap unit button first.
Calculate cos [degrees]
The identities of cosine -45° are as follows:
= sin (90° – 45°) = sin 45°
= sin (90° + 45°) = sin 135°
-cos-45°
= cos (180° – 45°) = cos 135°
= cos (180° + 45°) = cos 225°
There are more formulas for the double angle (2 × -45°), half angle ((-45/2)°) as well as the sum, difference and products of two angles such as -45° and β.
You can locate all of them in the respective article found in the header menu. To find everything about cos 45° click the link. And here is all about sin -45°, including, for instance, a converter.
In terms of the other five trigonometric functions, cos of -45° =
- $\pm \sqrt{1-\sin^{2} (-45 ^\circ)}$
- $\pm\frac{1}{\sqrt{1 + \tan^{2} (-45^\circ)}}$
- $\pm\frac{\cot (-45^\circ)}{\sqrt{1 + \cot^{2} (-45^\circ)}}$
- $\frac{1}{\sec (-45^\circ)}$
- $\pm\frac{\sqrt{\csc^{2} (-45^\circ) – 1} }{\csc (-45^\circ)}$
As the cosine function is the reciprocal of the secant function, 1 / sec -45° = cos-45°.
In the next part we discuss the trigonometric significance of cos minus 45°, and there you can also learn what the search calculations form in the sidebar is used for.
What is cos -45°?
In a circle with the radius r, the horizontal axis x, and the vertical axis y, -45 degrees is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.
As detailed in the unit-circle definition on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, x = cos -45°.
Note that you can locate many terms including the cosine-45° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of cos-45°.
Along the same lines, using the aforementioned form, can you look up terms such as cos -45° value, cos -45, cos-45° value and what is the cos of -45 degrees, just to name a few.
Given the periodic property of cosine of -45°, to determine the cosine of an angle < -360°, e.g. -765°, calculate cos -765° as cos (-765 Mod 360)° = cosine of -45°, or look it up with our form.
Conclusion
The frequently asked questions in the context include what is cos -45 degrees and what is the cos of -45 degrees for example; reading our content they are no-brainers.
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– Article written by Mark, last updated on February 26th, 2017