Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S6-SA2-0299
What is the Value of cos 90 degrees?
Grade Level:
Class 10
AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine
Definition
What is it?
The value of cos 90 degrees is a specific trigonometric ratio for a 90-degree angle. In a right-angled triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. For a 90-degree angle, this value is 0.
Simple Example
Quick Example
Imagine you are standing at the centre of a cricket field and looking straight towards the boundary. If you then turn exactly 90 degrees to your right or left, you are now looking along the boundary line. At this 90-degree turn, the 'cosine' effect, which measures how much you are still looking 'forward', becomes zero.
Worked Example
Step-by-Step
Let's find the value of cos 90 degrees using the unit circle method. --- Step 1: Draw a coordinate plane (x-axis and y-axis). --- Step 2: Draw a circle with its center at the origin (0,0) and a radius of 1 unit. This is called a unit circle. --- Step 3: Start from the point (1,0) on the positive x-axis. This represents an angle of 0 degrees. --- Step 4: Move counter-clockwise along the circle until the angle formed with the positive x-axis is 90 degrees. --- Step 5: At 90 degrees, you will reach the point (0,1) on the positive y-axis. --- Step 6: For any point (x,y) on the unit circle, cos(theta) is equal to the x-coordinate. --- Step 7: At 90 degrees, the x-coordinate is 0. --- Answer: Therefore, cos 90 degrees = 0.
Why It Matters
Understanding cos 90 degrees is crucial in fields like Physics for analyzing forces and motion, and in Engineering for designing structures. AI/ML algorithms use trigonometry for image processing and robotics, helping self-driving cars 'see' their surroundings and navigate safely.
Common Mistakes
MISTAKE: Confusing cos 90 degrees with sin 90 degrees or tan 90 degrees. | CORRECTION: Remember that cos 90 degrees is 0, while sin 90 degrees is 1 and tan 90 degrees is undefined.
MISTAKE: Thinking that cos 90 degrees is 1 because 90 is a 'big' angle. | CORRECTION: Cosine values range from -1 to 1. As the angle increases from 0 to 90 degrees, the cosine value decreases from 1 to 0.
MISTAKE: Not understanding the concept of adjacent side becoming zero for a 90-degree angle in a right triangle. | CORRECTION: Visualize a right triangle where one angle approaches 90 degrees. The adjacent side to that angle shrinks to zero length, making the ratio adjacent/hypotenuse equal to 0.
Practice Questions
Try It Yourself
QUESTION: What is the value of 5 * cos 90 degrees? | ANSWER: 0
QUESTION: If a ladder makes an angle of 90 degrees with the ground, what is the cosine of that angle? | ANSWER: 0
QUESTION: In a right-angled triangle, if one acute angle is 0 degrees, what would be the value of cos of the other acute angle? | ANSWER: 0 (Because if one acute angle is 0, the other acute angle must be 90 degrees, and cos 90 degrees is 0)
MCQ
Quick Quiz
What is the value of cos 90 degrees?
1
-1
Undefined
The Correct Answer Is:
B
The correct value for cos 90 degrees is 0. This can be understood by visualizing the unit circle or the definition of cosine in a right-angled triangle where the adjacent side becomes zero for a 90-degree angle.
Real World Connection
In the Real World
When ISRO launches rockets, engineers use trigonometry to calculate the trajectory and ensure the rocket reaches its target orbit. Understanding angles like 90 degrees and their cosine values helps in precisely determining the horizontal component of the rocket's position at different stages of flight.
Key Vocabulary
Key Terms
TRIGONOMETRY: A branch of mathematics dealing with the relations of the sides and angles of triangles | COSINE: A trigonometric ratio of the adjacent side to the hypotenuse in a right-angled triangle | UNIT CIRCLE: A circle with a radius of 1, centered at the origin of a coordinate plane | HYPOTENUSE: The longest side of a right-angled triangle, opposite the right angle
What's Next
What to Learn Next
Now that you know cos 90 degrees, try learning about sin 0 degrees and tan 45 degrees. These values are also fundamental and will help you solve more complex problems in trigonometry and understand how these ratios change with different angles.
