Understanding the Problem

This question presents four options with mathematical expressions and asks which one is correct. We need to evaluate each expression step by step.

Step 1: Analyze Option 1

Option 1 states "All are correct" - this is a meta-option that we can only verify after checking the others.

Step 2: Analyze Option 2

Expression: $\sin (\pi /2)=1$

This is correct because sine of 90° (π/2 radians) equals 1.

Step 3: Analyze Option 3

Expression: $\cos \left(0\right)=1$

This is correct because cosine of 0° equals 1.

Step 4: Analyze Option 4

Expression: $\tan (\pi /4)=1$

This is correct because tangent of 45° (π/4 radians) equals 1.

Step 5: Final Evaluation

Since options 2, 3, and 4 are all mathematically correct, option 1 ("All are correct") is the right answer.

Related Trigonometric Concepts

Trigonometric functions relate angles to ratios of sides in right triangles:

• Sine: opposite/hypotenuse
• Cosine: adjacent/hypotenuse
• Tangent: opposite/adjacent

Key Trigonometric Values

Important exact values to remember:

Final Answer

Option 1: "All are correct" is the right choice because all three trigonometric statements are mathematically accurate.