Sin 45 Degree Value

Sin 45 Degree Value is 1/√2 or \(\frac{1}{\sqrt{2}}\) and in the decimal form, it is 0.7071067812. So, if you are looking for Sin 45 degree value and other related concepts then you have landed on the right page. In the next few sections of this article, we will provide you with all the details on sin values for 0°, 30°, 45°, 60°, 90°…..360°. We will also provide a chart which you can save it in your phone and use it for revision purpose.

Sin 45 Degree or Sin 45° Value

Now let us know how the value of sin 45 is calculated and for this, we will require a right-angled (90°) triangle. In the below figure we have a right angle triangle QPR right-angled at Q. ‘a’ is the perpendicular, ‘b’ is the base and ‘h’ is the hypotenuse.

And we know that Sinθ = \(\frac{Perpendicular}{Hypotenuse}\) = \(\frac{a}{h}\).

So using the above we can calculate the values of various sin angles.

Sin 0° = \(\sqrt{\frac{0}{4}}\) = 0
Sin 30° = \(\sqrt{\frac{1}{4}}\) = ½
Sin 45° = \(\sqrt{\frac{2}{4}}\) = 1/√ 2
Sin 60° = \(\sqrt{\frac{3}{4}}\) = √3/2
Sin 90° = \(\sqrt{\frac{4}{4}}\) = 1

Sin 45 in Radians & Degrees

You can check the values from the table below:

Sine 0°	0
Sine 30° or Sine π/6	1/2
Sine 45° or Sine π/4	1/√2
Sine 60°or Sine π/3	√3/2
Sine 90°or Sine π/2	1
Sine 120°or Sine 2π/3	√3/2
Sine 150°or Sine 5π/6	1/2
Sine 180° or Sine π	0
Sine 270° or Sine 3π/2	-1
Sine 360°or Sine 2π	0

Sin Cos Tan Trigonometric Ratios Table

So now that you know the values for sin you can use the below method to find the values for other ratios as well:

Degrees	0°	30°	45°	60°	90°	180°	270°	360°
Sin	0	1/2	1/√2	√3/2	1	0	-1	0
Cos	1	√3/2	1/√2	1/2	0	-1	0	1
Tan	0	1/√3	1	√3	∞	0	∞	0

The above figure displays values of Sin and Cos functions from 0° to 330°.

Learn on Embibe

Students can access the following study materials on Embibe for their exam preparation:

NCERT Solutions	NCERT Books
Class 8 Mock Test Series	Class 8 Practice Questions
Class 9 Mock Test Series	Class 9 Practice Questions
Class 10 Mock Test Series	Class 10 Practice Questions
JEE Main Mock Tests (Class 11-12 PCM)	JEE Main Practice Questions (Class 11-12 PCM)
NEET Mock Tests (Class 11-12 PCB)	NEET Practice Questions (Class 11-12 PCB)

Value of Sin in 4 Quadrants

There are 4 quadrants starting from 0° and ending at 360°. The first quadrant is from 0° to 90°, the second quadrant is 90° to 180°, the third quadrant is 180° to 270° and 4th quadrant is 270° to 360°.

The values of sin, cos, tan, cosec, sec, cot varies depending on the quadrant where it lies.

	I	II	III	IV
Sin x	+	+	–	–
Cos x	+	–	–	+
Tan x	+	–	+	–
Cosec x	+	+	–	–
Sec x	+	–	–	+
Cot x	+	–	+	–

Functions of Negative Angles

Let θ be any angle. Then:

(i) sin (– θ) = – sin θ
(ii) cos (–θ) = cos θ
(iii) tan (– θ) = – tan θ
(iv) cot (–θ) = – cot θ sec (–θ) = sec θ
(v) cosec (– θ) = – cosec θ

Sin And Cos Formulas

Here are some formulas or identities that will help you in your preparation:

(a) sin (A + B) = sin A cos B + cos A sin B
(b) sin (A – B) = sin A cos B – cos A sin B
(c) cos (A + B) = cos A cos B – sin A sin B
(d) cos (A – B) = cos A cos B + sin A sin B

Frequently Asked Questions

Here are some questions that are commonly searched on the topic:

Q. What is the exact value of sin 45?
Ans. 0.7071067812 is the exact value of sin 45.

Q. What is sin 45 degrees in fraction?
Ans. The value of sin 45° in fraction is 1/√2.

Q. Are sin 45 and cos 45 the same?
Ans. Yes, the values of both sin and cos 45 are the same i.e 1/√2.

That was all on Sin 45 Degrees. We hope the information provided to you on this page was helpful. However, if you have further questions feel to use the comments section.