Math Problem Statement

Solve the following inverse trigonometric functions: sin⁻¹(2/3), tan⁻¹(4), and cos⁻¹(0.1).

Solution

It seems that the text extraction from the image wasn't successful. However, I can clearly observe the mathematical expressions from the image you provided. Let's break them down:

  1. sin1(23)=?\sin^{-1}\left(\frac{2}{3}\right) = ?^\circ
  2. tan1(4)=76\tan^{-1}(4) = 76^\circ
  3. cos1(0.1)=?\cos^{-1}(0.1) = ?^\circ

I'll calculate the missing values for the inverse sine and inverse cosine functions in degrees.

Let's start with:

sin1(23)\sin^{-1}\left(\frac{2}{3}\right) and cos1(0.1)\cos^{-1}(0.1)It seems like I can't do more advanced data analysis right now. Please try again later.

In the meantime, I can guide you through the steps to calculate sin1(23)\sin^{-1}\left(\frac{2}{3}\right) and cos1(0.1)\cos^{-1}(0.1) manually or using a calculator. Would you like those steps?

Here are five related questions:

  1. What is the general range of values for inverse sine and cosine functions?
  2. Can you explain the relationship between sine, cosine, and their inverse functions?
  3. What real-world applications use inverse trigonometric functions?
  4. How can you convert radians to degrees in inverse trigonometric calculations?
  5. How do you solve trigonometric equations involving inverse functions?

Tip: Always ensure your calculator is in the correct mode (degrees or radians) when working with trigonometric functions!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Inverse Trigonometric Functions
Sine Function
Cosine Function
Tangent Function

Formulas

sin⁻¹(x) = θ where sin(θ) = x
cos⁻¹(x) = θ where cos(θ) = x
tan⁻¹(x) = θ where tan(θ) = x

Theorems

Inverse Trigonometric Function Definitions
Pythagorean Identity

Suitable Grade Level

Grades 9-12